Limits and Derivation Questions

Question

1. Find the slope of tangent(s) line to the graph of f(x) = x^3-x+6 from the point P(-2,8)
2. find the value of K so limitation exists. lim as x->3 5x^2+8x-4/x^2-3x+K

Answer 1

Part 1

The derivative is 3x²-1 and its value at -2 is 11 which is the slope of the tangent line.

Part 2

Rational fractions are continuous except at zeroes of the denominator.

As long as K ≠ 0, the denominator is not zero and the limit will exist.