MTH102 Tma Solutions
1. Given that \( y=x^{-m}\) what is \(\frac{dy}{dx}\)?
\(\frac{-m}{x^{(m-1)}}\)
\(\frac{-mx^{(m+1)}}{x^{m-1}} \)
—>> \(\frac{-m}{x^{(m+1)}}\)
\(\frac{-{mx^{m-1}}}{x^{(m+1)}}\)
2. Let \(f \) and \(g\) be defined by \(f:x\rightarrow {3x-1})\ and\(g:x\rightarrow {2-5x}\). Find\(fog{(2)}\)
\(-20\)
\{-23\}
\{25\}
—>> \{-25\}
3. The distance s in meters covered by a particle in \(t\) seconds is \(s=\frac{3}{2} t^2-3t\). Find its acceleration.
—>> \(3ms^{-2}\)
\(1ms^{-2}\)
\(4ms^{-2}\)
\(2ms^{-2}\)
4. What is the derivative of \(\sqrt {x}\)
\(\frac{-1}{2\sqrt {x}}\)
—>> \(\frac{1}{2\sqrt {x}}\)
\(\frac{1}{\sqrt {x}}\)
\(\frac{-1}{\sqrt {x}}\)
5. If \(y=x^3-x^2-x+6\), find the values of \( x\) at the turning points.
—>> 1 and \(frac{-1}{3}\)
\(\frac{1}{3}\)
\(-1\) and \(\frac{-1}{3}\)
\(1\) and \(\frac{1}{3}\)
6. Find the gradient of the curve with equation \(2x^2-4xy+3y^2 = 3\) at the point (2,1).
4
3
1
—>> 2
7. Evaluate the integral \(\int_{2}^{4} (x^{2}-1) dx\)
\(48-log_eâ¡ 2\)
\(-48+log_eâ¡ 2\)
\(-48-log_eâ¡ 2\)
—>> \(48+log_eâ¡ 2\)
8. Given that\(x=2cos{\theta }\)and\(y=2sin{\theta }\) evaluate \(x^2+y^2\)
1
—>> 2
4
8
9. Find \(\lim_{x\rightarrow 1} (2x-3)\)
—>> \(-1\)
1
\(0\)
2
10. Evaluate \(int _{4}^{9} \frac{dx}{\sqrt{x}}\)
7
—>> 2
1
14
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