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Test: Calculus- 1 - Question 1

Let and denote the area of region bounded by f(x) and the X-axis, when varies from -1 to 1. Which of the following statements is/are TRUE?

I. is continuous in [-1, 1]

II. is not bounded in [-1, 1]

III. is nonzero and finite

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Test: Calculus- 1 - Question 4

A function f(x) is continuous in the interval [0,2] f(0) = f(2) = -1 and f(1) = 1. Which one of the following statements must be true?

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Test: Calculus- 1 - Question 6

Let f(x) be a polynomial and be its derivative. If the degree of is 10, then the degree of

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Test: Calculus- 1 - Question 7

Consider the following two statements about the function

- P. f(x) is continuous for all real values of .
- Q .f(x) is differentiable for all real values of .

Which of the following is TRUE?

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*Answer can only contain numeric values

Test: Calculus- 1 - Question 9

Let f be a function defined by

Find the values for the constants a, b,c and d so that f is continuous and differentiable everywhere on the real line.

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Test: Calculus- 1 - Question 10

Let the function

where denote the derivative of f with respect to θ. Which of the following statements is/are TRUE?

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Test: Calculus- 1 - Question 11

The function satisfies the following equation:

. The value of is______.

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Test: Calculus- 1 - Question 12

The formula used to compute an approximation for the second derivative of a function f at a point x_{0} is

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