6. (a) let f : R → R be a function defined by f(x) = x...

6. (a) let f : R → R be a function defined by
f(x) =

x + 4 if x ≤ 1
ax + b if 1 < x ≤ 3
3x x 8 if x > 3
Find the values of a and b that makes f(x) continuous on R. [10 marks]
(b) Find the derivative of f(x) = tann 1
1 ∞x
1 + x

. [15 marks]
(c) Find f
0
(x) using logarithmic differentiation, where f(x) = e
e 3x
√
2x x 5
(6 65x)
4
. [15 marks]
(d) Evaluate the integral Z
(x
3 + 1)1/3x
5
dx.

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Expert Solution

milcah answered 1 year ago

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