Calc questions?

Question

Let y=f(x) be a solution to the differential equation dy/dx = x + y. What is the approximation for f(2) if Euler's method is used, starting at x=1 with a step size of 0.5?

What are all the values of p for which integral 1/x^(2*p) dx converges from 0 to infinity?

What is the value of summation from n=1 to infinity, 2^(n+1) / 3^n?

The Maclaurin Series for 1/(1-x) is summation from n=0 to infinity, x^n. Write the first four terms of the power series expansion for x^2 / (1-x^2).

A curve C is defined by the parametric equations x=t^2-4t+1 and y=t^3. Write an equation for the line tangent to the graph of C at the point (-3,8).

Answer 1

A curve C is defined by the parametric equations x=t^2-4t+1 and y=t^3. Write an equation for the line tangent to the graph of C at the point (-3,8).

slope=m=dy/dx=(dy/dt)/(dx/dt)=3t^2 / (2t-4)

x=-3
y=8

t=2

m= 12/0=infinity


Hence
x=-3 is the tangent line