mathematics questions

MAT101 Final (Due May 12)

ID : _________________ Name: ___________________________________

[1] Evaluate f’(2) where

𝑓(𝑥) = 𝑒 2 ln 𝑥 + 𝑥

[2] Find the value of c if

𝑓(𝑥) = 𝑥𝑒 𝑐𝑥

and

𝑓′(0.5) = 0

[3] Evaluate the limit using L'Hôpital's rule

lim 𝑥→0

1 − 𝑒 −2𝑥

𝑥

[4] Find the maximum and minimum of the following function

𝑦 = 𝑥3 − 12𝑥

on the interval

−3 ≤ 𝑥 ≤ 3

[5] Evaluate the definite integral

∫ 𝑒 −

𝑥 2 𝑑𝑥

∞

0

[6] Find the value of k if

∫ 1

√𝑥𝑘 3

𝑑𝑥 = 3 1

0

[7] Find one possible value of x that satisfies the equation:

sin2(7) + cos2(x) = 1