A Set of Very Difficult Limitation and Derivation Questions

Question

1. Find the value of B if the graph y = b/x^2 has its tangent line defined by bx - 4y +21 = 0
2. Find the nth derivative f^(n) for f(x) = x/x+1
3. Find the value(s) of K for which lim x->3 5x^2+8x-4/x^2-3x+k
4. Given y= u^2-1/2u+1 and u=-2x^3+3x, find dy/dx where x=2

Answer 1

Part 1

y=b/x² => dy/dx=-2b/x³

The equation of the tangent line is y=(b/4)x+(21/4)

Therefore

-2b/x³ = b/4 and x=-2

Now the tangent line and the curve must meet at the point of tangency; therefore

(b/4)x+(21/4) = b/x²

Substitute the value of x into this equation and solve for b

Part 2

The first derivative is (x+1)^-2

The 2nd is -2(x+1)^-3

And this establishes the pattern

Part 3

What is your question?

Part 4

Use the chain rule.

It is a messy problem but straightforward...just be careful with algebra.