MTH232 Past Questions | Campusflava https://campusflava.com Tutors, Past Questions and Projects. Tue, 22 Feb 2022 11:33:47 +0000 en-US hourly 1 https://wordpress.org/?v=6.6.3 https://i0.wp.com/campusflava.com/wp-content/uploads/2023/01/cropped-CF.png?fit=32%2C32&ssl=1 MTH232 Past Questions | Campusflava https://campusflava.com 32 32 123014824 MTH232 Solutions https://campusflava.com/blog/mth232-solutions/ https://campusflava.com/blog/mth232-solutions/#respond Wed, 12 Jan 2022 09:53:55 +0000 https://campusflava.com/blog/mth232-solutions/ MTH232 Tma Solutions 1. In the special case in question (7) where \(x_0=0) this series is also called Fibonnaci sequence Taylor series —>> Maclaurin series all of the above 2. For the Legendre’s equation \(\large \((1-x^2)y{”}-2xy{‘}+\alpha (\alpha +1)y=0) what type of point is \(x_0=1)\)n —>> regular singular point Irregular point Singular point Irregular singular point […]

The post MTH232 Solutions first appeared on Campusflava.]]> MTH232 Tma Solutions

1. In the special case in question (7) where \(x_0=0) this series is also called

Fibonnaci sequence

Taylor series

—>> Maclaurin series

all of the above

2. For the Legendre’s equation \(\large \((1-x^2)y{”}-2xy{‘}+\alpha (\alpha +1)y=0) what type of point is \(x_0=1)\)n

—>> regular singular point

Irregular point

Singular point

Irregular singular point

3. \(\large A set of function \({f_0(x),f_1(x),…..,f_n(x),…})\) is said to be orthogonal wrt w(x) over the interval (a,b) if

—>> \(\large \( \int_{a}^{b}w(x)f_n(x)f_m(x)dx = \left\{ \begin{array}{ll} 1 & \mbox{if $m \neq n$};\\ 0 & \mbox{if $m=n$}.\end{array} \right. \)\)

\(\large \( \int_{a}^{b}w(x)f_n(x)f_m(x)dx = \left\{ \begin{array}{ll} 0 & \mbox{if $m \neq n$};\\ 1 & \mbox{if $m=n$}.\end{array} \right. \)\)

Both A and B

None of the above

4. If a function f has derivatives of all orders at a point \(\large \(x=x_0)\) then the Taylor series of f about \(x_0) is defined byn

\(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n!}\)\)

—>> \(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n!} (x-1)^n)\)\)

\(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n-1}\)\)

None of the above

5. Find the radius of convergence of the series \(\large \( \sum_{n=1}^\infty 2^nn^2(x-1)^2\)n

—>> \(\large \(R=\frac{1}{2})\)

\(\large \(R=\frac{1}{3})\)

\(\large \(R=\frac{3}{5})\)

\(\large \(R=\frac{1}{7})\)

6. If g(x) is an even function then \(\(\int_{-c}^{c}g(x)dx=?)\)n

\(\(\int_{2}^{c}g(x)dx)\)

—>> \(\(2\int_{0}^{c}g(x)dx)\)

\(\(2\int_{c}^{0}g(x)dx)\)

\(\(\int_{-2}^{0}g(x)dx)\)

7. \(Solve \(ay\frac{dy}{dx}+4x=0)\)

\(\(y=\sqrt\frac{2c-4x{2}}{18})\)

\(\(y=\sqrt\frac{2c-4x{2}}{3c})\)

—>> \(\(y=\sqrt\frac{2c-4x{2}}{9})\)

\(\(y=\sqrt\frac{5c-2x{2}}{9})\)

8. \(What is the order of the following DE \(\(\frac{dy}{dx})^2+2y=1\)

Second order

—>> First order

zero order

third order

9. What type of point is \(x_0=0) for the Bessel’s equation \(\large \(x^2y{”}+xy{‘}+(x^2-v^2)y=0)\)n

Singular point

Irregular point

Irregular singular point

—>> regular singular point

10. When is a D.E is said to be separable ?

—>> when it can be put in the form \(\(g(y)dy=f(x)dx)\)n

when it can be put in the form \(\frac{g(y)dy}{f(x)dx})\)n n

Both A and B

None of the above

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The post MTH232 Solutions first appeared on Campusflava.]]> https://campusflava.com/blog/mth232-solutions/feed/ 0 70694 When is a D.E is said to be separable ? https://campusflava.com/blog/when-is-a-d-e-is-said-to-be-separable/ https://campusflava.com/blog/when-is-a-d-e-is-said-to-be-separable/#respond Wed, 12 Jan 2022 09:51:06 +0000 https://campusflava.com/blog/when-is-a-d-e-is-said-to-be-separable/ When is a D.E is said to be separable ? —>> when it can be put in the form \(\(g(y)dy=f(x)dx)\)n when it can be put in the form \(\frac{g(y)dy}{f(x)dx})\)n n Both A and B None of the above

The post When is a D.E is said to be separable ? first appeared on Campusflava.]]> When is a D.E is said to be separable ?

—>> when it can be put in the form \(\(g(y)dy=f(x)dx)\)n

when it can be put in the form \(\frac{g(y)dy}{f(x)dx})\)n n

Both A and B

None of the above

The post When is a D.E is said to be separable ? first appeared on Campusflava.]]> https://campusflava.com/blog/when-is-a-d-e-is-said-to-be-separable/feed/ 0 70693 What type of point is \(x_0=0) for the Bessel’s equation \(\large \(x^2y{”}+xy{‘}+(x^2-v^2)y=0)\)n https://campusflava.com/blog/what-type-of-point-is-x_00-for-the-bessels-equation-large-x2yxyx2-v2y0n/ https://campusflava.com/blog/what-type-of-point-is-x_00-for-the-bessels-equation-large-x2yxyx2-v2y0n/#respond Wed, 12 Jan 2022 09:51:00 +0000 https://campusflava.com/blog/what-type-of-point-is-x_00-for-the-bessels-equation-large-x2yxyx2-v2y0n/ What type of point is \(x_0=0) for the Bessel’s equation \(\large \(x^2y{”}+xy{‘}+(x^2-v^2)y=0)\)n Singular point Irregular point Irregular singular point —>> regular singular point

The post What type of point is \(x_0=0) for the Bessel’s equation \(\large \(x^2y{”}+xy{‘}+(x^2-v^2)y=0)\)n first appeared on Campusflava.]]> What type of point is \(x_0=0) for the Bessel’s equation \(\large \(x^2y{”}+xy{‘}+(x^2-v^2)y=0)\)n

Singular point

Irregular point

Irregular singular point

—>> regular singular point

The post What type of point is \(x_0=0) for the Bessel’s equation \(\large \(x^2y{”}+xy{‘}+(x^2-v^2)y=0)\)n first appeared on Campusflava.]]> https://campusflava.com/blog/what-type-of-point-is-x_00-for-the-bessels-equation-large-x2yxyx2-v2y0n/feed/ 0 70692 \(What is the order of the following DE \(\(\frac{dy}{dx})^2+2y=1\) https://campusflava.com/blog/what-is-the-order-of-the-following-de-fracdydx22y1/ https://campusflava.com/blog/what-is-the-order-of-the-following-de-fracdydx22y1/#respond Wed, 12 Jan 2022 09:50:52 +0000 https://campusflava.com/blog/what-is-the-order-of-the-following-de-fracdydx22y1/ \(What is the order of the following DE \(\(\frac{dy}{dx})^2+2y=1\) Second order —>> First order zero order third order

The post \(What is the order of the following DE \(\(\frac{dy}{dx})^2+2y=1\) first appeared on Campusflava.]]> \(What is the order of the following DE \(\(\frac{dy}{dx})^2+2y=1\)

Second order

—>> First order

zero order

third order

The post \(What is the order of the following DE \(\(\frac{dy}{dx})^2+2y=1\) first appeared on Campusflava.]]> https://campusflava.com/blog/what-is-the-order-of-the-following-de-fracdydx22y1/feed/ 0 70691 \(Solve \(ay\frac{dy}{dx}+4x=0)\) https://campusflava.com/blog/solve-ayfracdydx4x0/ https://campusflava.com/blog/solve-ayfracdydx4x0/#respond Wed, 12 Jan 2022 09:50:45 +0000 https://campusflava.com/blog/solve-ayfracdydx4x0/ \(Solve \(ay\frac{dy}{dx}+4x=0)\) \(\(y=\sqrt\frac{2c-4x{2}}{18})\) \(\(y=\sqrt\frac{2c-4x{2}}{3c})\) —>> \(\(y=\sqrt\frac{2c-4x{2}}{9})\) \(\(y=\sqrt\frac{5c-2x{2}}{9})\)

The post \(Solve \(ay\frac{dy}{dx}+4x=0)\) first appeared on Campusflava.]]> \(Solve \(ay\frac{dy}{dx}+4x=0)\)

\(\(y=\sqrt\frac{2c-4x{2}}{18})\)

\(\(y=\sqrt\frac{2c-4x{2}}{3c})\)

—>> \(\(y=\sqrt\frac{2c-4x{2}}{9})\)

\(\(y=\sqrt\frac{5c-2x{2}}{9})\)

The post \(Solve \(ay\frac{dy}{dx}+4x=0)\) first appeared on Campusflava.]]> https://campusflava.com/blog/solve-ayfracdydx4x0/feed/ 0 70690 If g(x) is an even function then \(\(\int_{-c}^{c}g(x)dx=?)\)n https://campusflava.com/blog/if-gx-is-an-even-function-then-int_-ccgxdxn/ https://campusflava.com/blog/if-gx-is-an-even-function-then-int_-ccgxdxn/#respond Wed, 12 Jan 2022 09:50:41 +0000 https://campusflava.com/blog/if-gx-is-an-even-function-then-int_-ccgxdxn/ If g(x) is an even function then \(\(\int_{-c}^{c}g(x)dx=?)\)n \(\(\int_{2}^{c}g(x)dx)\) —>> \(\(2\int_{0}^{c}g(x)dx)\) \(\(2\int_{c}^{0}g(x)dx)\) \(\(\int_{-2}^{0}g(x)dx)\)

The post If g(x) is an even function then \(\(\int_{-c}^{c}g(x)dx=?)\)n first appeared on Campusflava.]]> If g(x) is an even function then \(\(\int_{-c}^{c}g(x)dx=?)\)n

\(\(\int_{2}^{c}g(x)dx)\)

—>> \(\(2\int_{0}^{c}g(x)dx)\)

\(\(2\int_{c}^{0}g(x)dx)\)

\(\(\int_{-2}^{0}g(x)dx)\)

The post If g(x) is an even function then \(\(\int_{-c}^{c}g(x)dx=?)\)n first appeared on Campusflava.]]> https://campusflava.com/blog/if-gx-is-an-even-function-then-int_-ccgxdxn/feed/ 0 70689 Find the radius of convergence of the series \(\large \( \sum_{n=1}^\infty 2^nn^2(x-1)^2\)n https://campusflava.com/blog/find-the-radius-of-convergence-of-the-series-large-sum_n1infty-2nn2x-12n/ https://campusflava.com/blog/find-the-radius-of-convergence-of-the-series-large-sum_n1infty-2nn2x-12n/#respond Wed, 12 Jan 2022 09:50:32 +0000 https://campusflava.com/blog/find-the-radius-of-convergence-of-the-series-large-sum_n1infty-2nn2x-12n/ Find the radius of convergence of the series \(\large \( \sum_{n=1}^\infty 2^nn^2(x-1)^2\)n —>> \(\large \(R=\frac{1}{2})\) \(\large \(R=\frac{1}{3})\) \(\large \(R=\frac{3}{5})\) \(\large \(R=\frac{1}{7})\)

The post Find the radius of convergence of the series \(\large \( \sum_{n=1}^\infty 2^nn^2(x-1)^2\)n first appeared on Campusflava.]]> Find the radius of convergence of the series \(\large \( \sum_{n=1}^\infty 2^nn^2(x-1)^2\)n

—>> \(\large \(R=\frac{1}{2})\)

\(\large \(R=\frac{1}{3})\)

\(\large \(R=\frac{3}{5})\)

\(\large \(R=\frac{1}{7})\)

The post Find the radius of convergence of the series \(\large \( \sum_{n=1}^\infty 2^nn^2(x-1)^2\)n first appeared on Campusflava.]]> https://campusflava.com/blog/find-the-radius-of-convergence-of-the-series-large-sum_n1infty-2nn2x-12n/feed/ 0 70688 If a function f has derivatives of all orders at a point \(\large \(x=x_0)\) then the Taylor series of f about \(x_0) is defined byn https://campusflava.com/blog/if-a-function-f-has-derivatives-of-all-orders-at-a-point-large-xx_0-then-the-taylor-series-of-f-about-x_0-is-defined-byn/ https://campusflava.com/blog/if-a-function-f-has-derivatives-of-all-orders-at-a-point-large-xx_0-then-the-taylor-series-of-f-about-x_0-is-defined-byn/#respond Wed, 12 Jan 2022 09:50:24 +0000 https://campusflava.com/blog/if-a-function-f-has-derivatives-of-all-orders-at-a-point-large-xx_0-then-the-taylor-series-of-f-about-x_0-is-defined-byn/ If a function f has derivatives of all orders at a point \(\large \(x=x_0)\) then the Taylor series of f about \(x_0) is defined byn \(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n!}\)\) —>> \(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n!} (x-1)^n)\)\) \(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n-1}\)\) None of the above

The post If a function f has derivatives of all orders at a point \(\large \(x=x_0)\) then the Taylor series of f about \(x_0) is defined byn first appeared on Campusflava.]]> If a function f has derivatives of all orders at a point \(\large \(x=x_0)\) then the Taylor series of f about \(x_0) is defined byn

\(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n!}\)\)

—>> \(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n!} (x-1)^n)\)\)

\(\large \( \sum_{n=0}^\infty \frac{f^n(x_0)}{n-1}\)\)

None of the above

The post If a function f has derivatives of all orders at a point \(\large \(x=x_0)\) then the Taylor series of f about \(x_0) is defined byn first appeared on Campusflava.]]> https://campusflava.com/blog/if-a-function-f-has-derivatives-of-all-orders-at-a-point-large-xx_0-then-the-taylor-series-of-f-about-x_0-is-defined-byn/feed/ 0 70687 In the special case in question (7) where \(x_0=0) this series is also called https://campusflava.com/blog/in-the-special-case-in-question-7-where-x_00-this-series-is-also-called/ https://campusflava.com/blog/in-the-special-case-in-question-7-where-x_00-this-series-is-also-called/#respond Wed, 12 Jan 2022 09:50:17 +0000 https://campusflava.com/blog/in-the-special-case-in-question-7-where-x_00-this-series-is-also-called/ In the special case in question (7) where \(x_0=0) this series is also called Fibonnaci sequence Taylor series —>> Maclaurin series all of the above

The post In the special case in question (7) where \(x_0=0) this series is also called first appeared on Campusflava.]]> In the special case in question (7) where \(x_0=0) this series is also called

Fibonnaci sequence

Taylor series

—>> Maclaurin series

all of the above

The post In the special case in question (7) where \(x_0=0) this series is also called first appeared on Campusflava.]]> https://campusflava.com/blog/in-the-special-case-in-question-7-where-x_00-this-series-is-also-called/feed/ 0 70686 For the Legendre’s equation \(\large \((1-x^2)y{”}-2xy{‘}+\alpha (\alpha +1)y=0) what type of point is \(x_0=1)\)n https://campusflava.com/blog/for-the-legendres-equation-large-1-x2y-2xyalpha-alpha-1y0-what-type-of-point-is-x_01n/ https://campusflava.com/blog/for-the-legendres-equation-large-1-x2y-2xyalpha-alpha-1y0-what-type-of-point-is-x_01n/#respond Wed, 12 Jan 2022 09:50:09 +0000 https://campusflava.com/blog/for-the-legendres-equation-large-1-x2y-2xyalpha-alpha-1y0-what-type-of-point-is-x_01n/ For the Legendre’s equation \(\large \((1-x^2)y{”}-2xy{‘}+\alpha (\alpha +1)y=0) what type of point is \(x_0=1)\)n —>> regular singular point Irregular point Singular point Irregular singular point

The post For the Legendre’s equation \(\large \((1-x^2)y{”}-2xy{‘}+\alpha (\alpha +1)y=0) what type of point is \(x_0=1)\)n first appeared on Campusflava.]]> For the Legendre’s equation \(\large \((1-x^2)y{”}-2xy{‘}+\alpha (\alpha +1)y=0) what type of point is \(x_0=1)\)n

—>> regular singular point

Irregular point

Singular point

Irregular singular point

The post For the Legendre’s equation \(\large \((1-x^2)y{”}-2xy{‘}+\alpha (\alpha +1)y=0) what type of point is \(x_0=1)\)n first appeared on Campusflava.]]> https://campusflava.com/blog/for-the-legendres-equation-large-1-x2y-2xyalpha-alpha-1y0-what-type-of-point-is-x_01n/feed/ 0 70685