Calculus Answers

find fourier integral for the following f(x)= e-x x>0

(a) Find the derivative of the function 𝑦 = 2𝑥^2+12/x^2, when 𝑥 = 2.

(b) Let 𝑓(𝑥) = −3/𝑥−7. Find the inverse of the function.

Question 6 [2]

State the mean Value Theorem.

Question 5 [2;2]

Investigate whether the following functions are odd or even.

(a) 𝑓(𝑥) = 𝑥^

3

(b) 𝑓(𝑥) = cos 𝑥

Question 4 [7]

Prove that 𝑓(𝑥) = 𝑥^2 + 2𝑥 is not injective.

Question 2 [7]

Use sign table to determine the values of 𝑥 for which

x^2 + 9𝑥 + 20 ≤ 0.

Consider the relation 𝑃 = {(1,7), (−1,7), (3,9), (1,3)}. Is 𝑃 a function? Justify

your answer

F(x) = 6x² - 10x + 12

F(x) = 5x² -8x + 10

F(x) = x² + 9x - 4