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1)Using the definition of a derivative, i.e., the limit of the difference quotient, find LaTeX: f'left(aright)and the equation of the line tangent to the graph at the given value for

a

. LaTeX: fleft(xright)=sqrt[]{3x}, LaTeX: a=3.

2)A circle has an initial radius of 50 ft when the radius begins decreasing at a rate of 2 ft/min. What is the rate of change of the area at the instant the radius is 10 ft?

3)Find the derivative of the following functions.

a) LaTeX: y=left(x^2-2xright)log_3left(7xright)


b) LaTeX: y=frac{xe^{2x}}{sin x}




c) LaTeX: y=x^{sqrt[]{x+1}}






d) LaTeX: y=sec^{-1}left(3x^{frac{1}{2}}right)


4)Evaluate the following limit. LaTeX: lim_{xlongrightarrow0}frac{sin x}{sin5x}




5)Given LaTeX: x=cosleft(x-yright), find LaTeX: frac{dy}{dx}

6)Use the graph of LaTeX: gleft(xright)to answer the following questions.

Graph

a)Find the values of x in LaTeX: left(-2,2right)at which LaTeX: gleft(xright)is not continuous. Explain why.

b)Find the values of x in LaTeX: left(-2,2right)at which LaTeX: gleft(xright)is not differentiable. Explain why.

7)Find and simplify LaTeX: y^{''}. LaTeX: xy+y^2=1

 
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