Question Type 4: Finding parameter values so that a limit exists (using L’Hôpital) Exercises

Determine in terms of $k$:

and state for which $k$ it exists.

Find $k$ such that the limit exists and determine its value:

Determine

and state for which $k$ this limit exists.

Find all $k$ such that the limit exists:

Determine $k$ so that the limit is finite and compute it:

Find the values of $k$ such that the limit exists:

For which integer values of $k$ does the following limit exist, and what is its value?

Find the value of $k$ such that the following limit exists, and compute the limit:

$\lim_{x\to0}\frac{k x^2 + x\sin x - x^2}{x^3}$

Find $k$ such that the limit exists and calculate it:

Let $a$ be a constant. Find $b$ so that the limit exists and compute it: