Chapter 5: Differential Calculus March 14, 2024 Maven Leave a Comment Welcome to the Chapter 5: Differential Calculus Name Email 1. If y$=e^{2x}$, then $\frac{d^{2}y}{dx^{2}}$ at x=0 is 4 9 2 0 None 2. If y = x and z =$\frac{1}{x}$, then $\frac{dy}{dx}$= $x^{2}$ 1 -$x^{2}$ $-\frac{1}{x^{2}}$ None 3. $\frac{d}{dx}(a^{x})$ = $\frac{1}{xlog_{e}a}$ $a^{a}$ $x log_{e}a$ $a^{x}log_{e}a$ None 4. $\frac{d}{dx} (5e^{x}-2log x)$ is equal to $5e^{x}-\frac{2}{x}$ $5e^{x}-2x$ $5e^{x}-\frac{1}{x}$ 2 log x None 5. If y=$log x$, then $y_{2}$= $\frac{1}{x}$ $-\frac{1}{x^{2}}$ $-\frac{2}{x^{2}}$ $e^{2}$ None 6. For what value of x, f(x)=$\frac{x+2}{x-1}$ not continuous? -2 1 2 -1 None 7. If f(x)$=x^{2}$ and g(x)$= 2x+1$, the $f(g)(0)$ is 0 2 1 4 None 8. f(x) =$-5$ for all $x\in R$ is an identity function a modulus function an exponential function a constant function None 9. $\lim_{\theta\to 0} \frac{tan \theta}{\theta}=$ 1 $\infty$ -$\infty$ $\theta$ None 10. Which of the following function is neither even nor odd? $f(x)=x^{3}+5$ $f(x)=x^{5}$ $f(x)=x^{10}$ $f(x)=x^{2}$ None 11. $\frac{d}{dx}(\frac{1}{x})$ is equal to $\frac{-1}{x^{2}}$ $-\frac{-1}{x}$ $log (x)$ $\frac{1}{x^{2}}$ None 12. If the function f(x) is continuous at x = a, then $\lim_{x\rightarrow a} f(x)$ is equal to f(-a) $f(\frac{1}{a})$ 2f(a) f(a) None 13. The graph of f(x)=$e^{x}$ is identical to that of $f(x)=a^{x}, a> 1$ $f(x)=a^{x}, a< 1$ $f(x)=a^{x}, 0< a< 1$ y=ax+b, $a\neq 0$ None 14. The range of f(x)$= \left |x \right |$, for all $x\in R$ is $(0,\infty)$ $[0,\infty)$ $(-\infty,\infty)$ $[1,\infty)$ None 15. $\lim_{x\to 0} \frac{e^{x}-1}{x}$= e $nx^{n-1}$ 1 0 None 16. The graph of y $=2x^{2}$ is passing through (0,0) (2,1) (2,0) (0,2) None 17. f(x) $=\left\{\begin{matrix}x^{2}-4 if x\geq 2 \\ x+2 if x< 2 \end{matrix}\right.$, then f (5) is -1 2 5 7 None 18. If f(x)=$2^{x}$ and g(x)=$\frac{1}{2^{x}}$, then f(g)(x)is 1 0 $4^{x}$ $\frac{1}{4^{x}}$ None 19. If f(x) $= x^{2} - x + 1$,then f(x+1) is $x^{2}$ x 1 $= x^{2} + x + 1$ None 20. The graph of the line y = 3 is Parallel to x-axis Parallel to y-axis Passing through the origin Perpendicular to x-axis None 21. f(x)=$\left\{\begin{matrix}x^{2}-4 if x\geq 2\\ x+2if x< 2 \end{matrix}\right.$, then f (0) is 2 5 -1 0 None 22. The graph of y=$e^{x}$ intersect the y-axis at (0, 0) (1, 0) (0, 1) (1, 1) None 23. Which one of the following functions has the property f(x) $=f\frac{1}{x}$, provided $x \neq 0$ $f(x)=\frac{x^{2}-1}{x}$ $f(x)=\frac{1-x^{2}}{x}$ f(x)$=x$ $f(x)=\frac{x^{2}+1}{x}$ None 24. The minimum value of the function f(x)=$\left |x \right |$ is 0 -1 1 -$\infty $ None 25. f(x) $=\frac{1-x}{1+x}, x> 1$, then f (-x) is equal to - f (x) $\frac{1}{f(x)}$ $-\frac{1}{f(x)}$ f (x) None Time's up Related Posts:Chapter 4: Differential EquationsChapter 2: Integral Calculus IChapter 3: Integral Calculus IIChapter 1: Introduction to Micro Economics
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