FBQ1: When the sequence of partial sums tends to an infinite limit, oscillates either finitely or infinitely the series is said to be ____
Answer: divergent
FBQ2: Both Taylor series and Maclaurin series only represent the function f(x) in their interval of ______
Answer: Convergence
FBQ3: When functions are expanded at x = a, we have Taylor’s expansion and when functions are expanded at x = 0 then we have _____ expansion
Answer: Maclaurin
FBQ4: By considering the hypothesis of mean value theorem, Given that f(x) = x2 + 2x +1 a = 1, b =2
Answer: 4
FBQ5: By considering the hypothesis of mean value theorem, Given that fx=x2+2x+1 and a=1, b = 2 find fb=_____
Answer: 9
FBQ6: By considering the hypothesis of mean value theorem, Given that fx=x2+2x+1 and a=1, b = 2 find fıc=_____
Answer: 5
FBQ7: _____ rule is a technique for approximating the definite integral
Answer: Trapezoidal
FBQ8: _____ rule is an arithmetical rule for estimating the area under a curve where the values of an odd number of ordinates including those at each end.
Answer: Simpson’s
FBQ9: The trapezoidal rule is also known as ____ rule
Answer: Trapezium
FBQ10: The ∂2f∂x∂y of the function fx,y=3x2-x3y3+5xy+6y3 evaluate at the points x=1 and y=2 is ___________
Answer: -31
FBQ11: The ∂2f∂y2 of the function fx,y=3x2-x3y3+5xy+6y3 evaluate at the points x=1 and y=2 is ___________
Answer: 60
FBQ12: The limx→2 x2-2xx2-4 is ___________
Answer: ½
FBQ13: The limx→∞ xx3+5 is ___________
Answer: 0
FBQ14: If fx=x(x2-x-2) satisfies Mean Value Theorem , the value c is ___________
Answer: 1/3
FBQ15: The exponential form of the function fx=1+x+x22!+x33!+x44!+x55!+⋯ is _______
Answer: exp x
FBQ16: Find the limit of \[\lim_{(x, y)\rightarrow (2, 1)} x+3y^{2}\] is ________
Answer: 5
FBQ17: Find the limit of \[\lim_{(x, y)\rightarrow(2,4)} \frac{x+y}{x-y}\] is ________
Answer: -3
FBQ18: Find limit \[\lim_{(x, y, z)\rightarrow (1, 2, 5)} \sqrt(x+y+z)\] is __________
Answer: 3
FBQ19: The coefficient of $$x^{2}$$ in the Taylor series about $$x=0$$ for $$f(x)=e^{-x^{2}}$$ is _____________
Answer: -1
FBQ20: The coefficient of $$x^{3}$$ in the Taylor series about x=0 for f(x)=sin 2x is _______________
Answer: -4/3
FBQ21: Let \[f(x)=\frac{\sin x}{1+x^{2}}\] and $$y^{n}$$ denote the $$n^{th}$$ derivative of f(x) at x=0 then the value of $$y^{100}+900y^{98}$$ is _________
Answer: 0
FBQ22: If the first derivative at x=0 of the function $$f(x)=\frac{\cos (x)}{x^{2}-x+1}$$ is ______
Answer: 2
FBQ23: Given $$f(x,y)= 2x^{2}y$$, the value $$\frac{\partial f(x,y)}{\partial x}$$ at x=2 and y=4 is ________
Answer: 24
FBQ23: .Given that the function $$f(x)=\frac{2(x+3)}{x^{2}+x-2}$$ has an absolute maximum on the -2<x<q. The maximum value is ________
Answer: 2
FBQ25: The points of inflection of the function $$ f(x)=x^{4}-12x^{3}+6x-9$$ on the interval $$-2\leq x\leq 10$$ are ____________ and _________
Answer: 0, 6
FBQ26: The value of a such that the function $$f(x)=x^{2}+ax+5, when f(2)= 15 is _______
Answer: 3
FBQ27: If x2+y2-2x-6y+5=0, the value d2ydx2 at x=3, y=2 is _____
Answer: 5
FBQ28: If the Mean Value Theorem satisfies fx=x2 on the interval -2, 1 , then the value of c is _____
Answer: -1/5
FBQ29: The minimum value of $$f(x,y)=x^{2}+y^{2}+6x+12$$ is _________
Answer: 3
FBQ30: Suppose w=x3yz+xy+z+3 and x=3cost, y=3sint and w=2t. The value dwdtt=π2 is _____________
Answer: 7
FBQ31: Let $$f(x)=\frac{e^{x} sin(x^{2})}{x}$$, then the value of the fifth derivative at x=0 is ___________
Answer: 21
FBQ32: Leibniz rule gives the Nth derivative of multiplication of _____ functions
Answer: Two
FBQ33: Leibniz theorem is applicable if n is a ________ integer
Answer: Positive
FBQ34: If nth derivative of $$xy_{3}+x^{2}y_{2}+x^{3}y_{0}=0$$ then order of its nth differential equation is _________
Answer: n+3
FBQ35: For the function $$f(x)=\frac{sin x}{x^{2}}$$. ________ are the number of points exist in the interval $$[0, 7\pi]$$ such that $$f’(c)= 0$$
Answer: True
FBQ36: $$f(x)=\frac{sin x}{x}$$. ________ are the number of points exist in the interval $$[0, 18\pi]$$ such that $$f’(c)= 0$$
Answer: 18
FBQ37: For all second degree polynomials with y = ax2 + bx + k, it is seen that the Rolles’ point is at c = 0. Also the value of k is zero. Then the value of b is _____
Answer: 0
FBQ38: For second degree polynomial it is seen that the roots are equal. Then ______ is the relation between the Rolles point c and the root x
Answer: c=x
FBQ39: Rolle’s Theorem is a special case of ___________ theorem
Answer: Mean value
FBQ40: The value of $$c$$ if $$f(x)=x(x-3)e^{3x}$$, is continuous over interval [0, 3] and differentiable over interval (0, 3)_________ (Answer to 3 decimal)
Answer: 2.703
FBQ41: The value of ‘a’ are _____ and ______,if f(x) = ax2+32x+4 is continuous over [-4, 0] and differentiable over (-4, 0) and satisfy the Rolle’s theorem. Hence find the point in interval (-2,0) at which its slope of a tangent is zero
Answer: 8, -2
FBQ42: For the function f(x) = x2 – 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes___________
Answer: 3/2
FBQ43: If f(a)=f(b) in mean value theorem, then it becomes ________ theorem
Answer: Rolle’s
FBQ44: Mean Value theorem is applicable to the functions continuous in closed interval [a, b] and ___________ in open interval (a, b)
Answer: Differentiable
FBQ45: Mean Value theorem is also known as ___________ theorem
Answer: Lagrange’s
FBQ46: The point c is _________ in the curve f(x) = x3 + x2 + x + 1 in the interval [0, 1] where slope of a tangent to a curve is equals to the slope of a line joining (0,1)
Answer: 0.54
FBQ47: _________ is the point c between [2,9] where, the slope of tangent to the function f(x)=1+∛x-1 at point c is equals to the slope of a line joining point (2,f(2)) and (9,f(9)).(Providing given function is continuous and differentiable in given interval).
Answer: 4.56
FBQ48: _______ is the point c between [-1,6] where, the slope of tangent to the function f(x) = x2+3x+2 at point c is equals to the slope of a line joining point (-1,f(-1)) and (6,f(6)).(Providing given function is continuous and differentiable in given interval).
Answer: 2.5
FBQ49: The necessary condition for the maclaurin expansion to be true for function f(x) is f(x) should be continuous and ______
Answer: Differentiable
FBQ50: The limit $$\lim_{(x, y)/rightarrow (0, 0)} \frac{x^{3}-y^{3}}{x-y}$$ is _______
Answer: 0
MCQ1: A single valued function of x is said to be continuous at x=a if
Answer: lim fx= f(a)
MCQ2: Which of the following is discontinuous at x = 0
Answer: Sin xx
MCQ3: A function y = f(x ) is said to be differentiable at a point x = a if
Answer: f1(x) exists that point
MCQ4: Find the derivative of y = Sin-1x
Answer: 11- x2
MCQ5: Suppose u = f(x, y) = x2 + y2, where x = cosh4t and y = 2t + t2. Find the total derivative of u with respect to t
Answer: 4sinh8t + 8t + 12t2 + 4t3
MCQ6: If f(u) = Sin u and u = x2+y2 find fx
Answer: Cos U1+x2
MCQ7: If f(u) = Sinu and u = x2+y2 find fy
Answer: y Cos Ux2+y2
MCQ8: Partial derivatives are said to be continuous if
Answer:
MCQ9: Obtain the slope of the tangent at the point (2,3) of the curve 6 x2 + 3xy + x4 + 3y2 = 0
Answer: -65 24
MCQ10: A function f (x, y) of two variables is said to have a local maximum at (a,b) if there exists a rectangular region containing (a,b) such that ____
Answer: f(x, y)≤ f(a, b)
MCQ11: The local maxima and minima are called the ____ of (x, y)
Answer: extreme
MCQ12: To test for critical point if fxxfyy - fxy2< 0 then this gives
Answer: saddle point
MCQ13: Obtain the stationary points of f(x, y) = x2+y2 subject to the constraint condition 3x+2y = 6
Answer: 18 13 ,12 13
MCQ14: A function f(x, y) is said to be homogeneous of degree m if
Answer: f(kx, ky) = km f(x, y)
MCQ15: What is the degree of the function f(x, y) = x3+4xy2- 3y3
Answer: three
MCQ16: If x and y are rectangular Cartesian coordinates, u = f(x, y) satisfies laplace’s equation if
Answer: ∂2f∂x2 + ∂2f∂y2 = 0
MCQ17: A function f(x, y) is said to have a maximum value of point (x, y) = (a, b) if
Answer: f(a+h, b+k)-f(a, b)<0
MCQ18: A function f(x, y) is said to have a minimum value of point (x, y) if
Answer: f(a+h, b+k)- f(a, b)>0
MCQ19: If exy+x+y=1, evaluate dy dx at (0,0)
Answer: -1
MCQ20: If xy + Sin y = 2 find dy dx
Answer: -y x+Cos y
MCQ21: If z= Sin (x+y), x = u2+ v2, y=2uv. Evaluate dzdu
Answer: 2(u+v) Cos(x + u)
MCQ22: With the usual notation a series cannot be convergent unless
Answer: limn→∞Un=0
MCQ23: Let U1+ U2+ . . . Un+ . . . be a series of positive terms. If limn→∞Un+1Un>1. Then the series
Answer: Diverges
MCQ24: As n→∞ of the series 1+12+13+14+ . . . is
Answer: divergent
MCQ25: For the series 12+23+34+45+ . . . an expression of Un+1 is given by
Answer: n+1n+2
MCQ26: By considering the D’ Alembert test for positive terms if limn→∞Un+1Un=1, then the series is
Answer: inconclusive
MCQ27: By the comparison test, the series 11P+12P+13P+14P + . . . +1nP ___ if p > 1
Answer: converges
MCQ28: Find limn→∞Sin2xx2
Answer: 1
MCQ29: Evaluate limx→0Sinhx-Sinxx3
Answer: 1/3
MCQ30: The Taylor’s series is given by
Answer: fx+h= fx+hfıx+h2fıı(x)2!+ . . .
MCQ31: Find limx→0tanx-xx3
Answer: 1/3
MCQ32: Determine limx→1 x3-2x2+4x-34x2-5x+1
Answer: 1
MCQ33: Find the second order derivatives of the function. fx=x2-cosx at x=π4
Answer: 2+12
MCQ34: Find the third order derivatives of the function. fx=x2-cosx at x=π4
Answer: -12
MCQ35: limx→0tanx-xSin x-x is
Answer: -2
MCQ36: From the Taylor’s expansion of Cos π3+x in ascending powers of x up to the x3 term find fı π3
Answer: -32
MCQ37: From the Taylor’s expansion of Cos π3+x in ascending powers of x up to the x3 term find fıı x
Answer: -cosx
MCQ38: From the Taylor’s expansion of Cos π3+x in ascending powers of x up to the x3 term find fıv π3
Answer: ½
MCQ39: From the Taylor’s expansion of Cos π3+x in ascending powers of x up to the x3 term find fıv x
Answer: Cosx
MCQ40: Suppose fx is a function continuous on a close interval a≤x≤b and differentiable on the open interval a<x<b and if fa= fb= 0, then fıc
Answer: 0
MCQ41: From the Maclaurin expansion fx=In(1+x) find fıııx
Answer: 21+x3
MCQ42: From the Maclaurin expansion fx=In(1+x) find fıvx
Answer: -6(1+x)4
MCQ43: From the Maclaurin expansion fx=In(1+x) find fıı0
Answer: -1
MCQ44: From the Maclaurin expansion fx=In(1+x) find fv0
Answer: 4!
MCQ45: Using Simpson’s rule with 6 equally spaced intervals and by considering the integral ∫064+x3dx. Find The number of ordinates
Answer: 7
MCQ46: Using Simpson’s rule with 6 equally spaced intervals and by considering the integral ∫064+x3dx. Find ∆x = strip width
Answer: 1
MCQ47: Using Simpson’s rule with 6 equally spaced intervals and by considering the integral ∫064+x3dx. Find Area
Answer: 22.6square units
MCQ48: The two segment trapezoidal rule of integration is exact for integrating at most ____ order of polynomial
Answer: first
MCQ49: Using trapezoidal rule with five (5) equally spaced intervals and by considering the integral. ∫12 1x dx. Evaluate b-an
Answer: 1/5
MCQ50: Using trapezoidal rule with five (5) equally spaced intervals and by considering the integral. ∫12 1x dx, evaluatethe area of the integral
Answer: 17532520