The following limit represents the derivative of some function
f
at some number
a
. State such an
f
and
a
. (3 marks)
\lim_(h->0)((2+h)^(3)-8)/(h)
Use the limit definition of derivative to find the derivative of
f(x)=1+x-2x^(2)
. (4 marks) Find the following limit (3 marks).
\lim_(t->0)(sin8t)/(sin9t)
Differentiate. (8 marks) a)
y=sin^(2)(cos4x)
b)
y=\root(4)((1-3t)^(3)+e^(2t))
Find
(dy)/(dx)
by implicit differentiation. (5 marks)
\sqrt(1+x^(2)y^(2))=2xy

Question

The following limit represents the derivative of some function

f

at some number

a

. State such an

f

and

a

. (3 marks)

\lim_(h->0)((2+h)^(3)-8)/(h)

Use the limit definition of derivative to find the derivative of

f(x)=1+x-2x^(2)

. (4 marks) Find the following limit (3 marks).

\lim_(t->0)(sin8t)/(sin9t)

Differentiate. (8 marks) a)

y=sin^(2)(cos4x)

b)

y=\root(4)((1-3t)^(3)+e^(2t))

Find

(dy)/(dx)

by implicit differentiation. (5 marks)

\sqrt(1+x^(2)y^(2))=2xy

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