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  3. 6. (a) let f : r ? r be a function defined by f(x)

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

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Basic Math

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. [10marks]
(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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