Calculus and vectors(CURVE SKETCHING)

Please show all work in mathematical format/steps so I can understand, thank you so much.

1. Determine any vertical asymptotes of the functionf(x)=x2+x2x then, find the one-sided limits approaching the vertical asymptotes.

2. For each of the following, check for discontinuities, then state and use at least two other tests to make a rough sketch of the curve.

a)y=x+5x3 b)f(x)=(x+2)25

c)g(t)=t5t22t15 d)y=(x23x)(2+x)(32x)

3. Use the algorithm for curve sketching to sketch the graph off(x)=3x32x2+5x

4. Use the y-intercept, local extrema, intervals of concavity, and points of in function to graphf(x)=4x3+6x224x2