Question

For each of the following limits, find the value or explain why it does not exist.

i) limₕ→₀f(5h)-f(5)/h

Answer 1

To find the limit limₕ→₀f(5h)-f(5)/h, substitute h=0 into the expression and see if it is defined. If f(x) is not given, we cannot determine the value and the limit does not exist.

Step-by-step explanation:

To find the limit limₕ→₀f(5h)-f(5)/h, we need to plug in h=0 into the expression and see if it is defined. Let's evaluate the expression step by step:

1. Start by substituting h=0 into the expression: f(5*0)-f(5)/0
2. The numerator, f(5*0)-f(5), becomes f(0)-f(5)
3. However, since f(x) is not given, we cannot determine the value of f(0) or f(5). Therefore, we cannot simplify the expression further and the limit does not exist.