Calculus& Analytical Geometry

Q1: Find the derivative of the following functions using the rules:
a) ????(????) = √2???? + 1
b) ???? =
????
2????+1
Q2: Find the critical point.
• ????(????) = ????
2 + 2???? + 1
10 M
2
Q3: Use the mean value theorem to find c:
a) ????(????) = 3 + √ ???? ???????? [0 , 4]
Q4: find the antiderivative of the following functions:
a) ????(????) = 4???? − 3
b) ????(????) = 8 ????
3 + 12
Q5: Evaluate the following integrals by using the given
substitutions:
a) ∫ ????
3
(????
4 − 1)
2 ????????, ???? = ????
4 − 1
3

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