Answer to Question #124129 in Calculus for Dereck Cole

Question

(a) let f : R → R be a function defined by
f(x) =



x + 4 if x ≤ 1
ax + b if 1 < x ≤ 3
3x − 8 if x > 3
Find the values of a and b that makes f(x) continuous on R.
(b) Find the derivative of f(x) = tan−1
1 − x
1 + x

.
(c) Find f
0
(x) using logarithmic differentiation, where f(x) = e
−3x
√
2x − 5
(6 − 5x)
4
.
(d) Evaluate the integral Z
(x
3 + 1)1/3x
5
dx.

Answer 1

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