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Engineering Math Practice Test: Differential Calculus
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Differential Calculus topics include: Leibniz rule, nth derivatives, rolles and lagrange mean value theorem, taylor mclaurin series, indeterminate forms, curvature, evolutes, envelopes, polar curves, arc length derivation, area derivatives, angle between radius vector and tangent, cauchy’s and generalized mean value theorem. Differential calculus is a branch of calculus that studies the rate of change of one variable in relation to another. It is a tool for analyzing mathematical problems, such as finding solutions to equations and understanding the behavior of curves and... Show more
Engineering Math Practice Test: Differential Calculus
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25 Questions

1. For the infinitely defined discontinuous function
\(\begin{cases}x+sin(2x)& :x\in [0,\pi] \\ x+sin(4x)& :x\in (\pi,2\pi] \\ x+sin(6x)& :x\in (2\pi,3\pi] \\.\\.\\x+sin(2nx)& :x\in [(n-1)\pi,n\pi)\\.\\.\end{cases}\)
How many points c∈[0,16x] exist, such that f'(c) = 1
2. The Mean Value Theorem was stated and proved by _______
3. The expansion of f(x,y), is
4. Nth derivative of \(\frac{1}{(1+x^2)}\)?
5. For the given function f(x)=\(\sqrt{x^3+x^7}\) the values of first and second derivative at x = 1 are assumed as 0 and 1 respectively. Then the value of the third derivative could be
6. L’Hospital Rule states that
7. nth derivative of Sinh(x) is
8. Which of the following is true
9. Function has the property that f(n) (x) = f(n + 2) (x) : n ≥ 1 : n ∈ N Then which of the following is the expression for f(x) in most general form.
10. What is the largest possible value of f(0), where f(x) is continuous and differentiable on the interval [-5, 0], such that f(-5)= 8 and f'(c)≤2.
11. For a third degree monic polynomial, it is seen that the sum of roots are zero. What is the relation between the minimum angle to be rotated to have a Rolles point (α in Radians) and the cyclic sum of the roots taken two at a time c
12. Mean Value Theorem tells about the
13. Expansion of function f(x) is?
14. Cauchy’s Mean Value Theorem is also known as ‘Extended Mean Value Theorem’.
15. f(x) = 3Sin(2x), is continuous over interval [0,π] and differentiable over interval (0,π) and c ∈(0,π)
16. The expansion of f(x, y)=ex Sin(y), is
17. Let f(x) = (x2 + x + 1)sinh(x) the (1097)th derivative at x = 0 is
18. Let f(x) = \(\sqrt{sin(x)}\) and let yn denote the nth derivative of f(x) at x = 0 then the value of the expression 12y(5) y(1) + 30 y(4) y(2) + 20 (y(3))2 is given by
19. Leibniz rule gives the
20. Let f(1) (n) = g(n) (0) for some functions f(x) and g(x). Now let the coordinate axes having graph f(x) be rotated by 45 degrees (clockwise). Then the corresponding Mclaurin series of transformed g(x) is?
21. If y=x4⁄x2-1, then?
22. What is the value of c which lies in [1, 2] for the function f(x)=4x and g(x)=3x2?
23. To find the value of sin(9) the Taylor Series expansion should be expanded with center as ___________
24. If the first and second derivatives at x = 0 of the function f(x)=\(\frac{cos(x)}{x^2-x+1}\)
were 2 and 3 then the value of the third derivative is
25. Find the value of ln(sin(31o)) if ln(2) = 0.69315

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