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Consider the function f(x)=3x2+2x.
Using the limit definition of the derivative, find f′(x).
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The function h is defined by
Find h′(x).
Determine the gradient of the curve y=h(x) at x=2.
Determine the equation of the tangent to y=h(x) at x=2 in the form ax+by+d=0, where a,b,d∈Z.
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Consider the function
and the following tables of values as x approaches 3 from below.
State x→3limf(x).
Explain why f(3) is undefined.
Determine the value of k.
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Consider the curve defined by
Find dxdy.
The point P lies on the curve with x=1.
Find the gradient of the tangent line at P.
Hence determine the equation of the normal to the curve at P in the form y=mx+c.
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