let $f(x) = 4x-13$
How do I simplify the limit below to find if it exists? $$\lim_{h\to0}\dfrac{f(x+h)-f(x)}{h}$$
The limit involves two variables and I'm unable to remove $h$ from the denumerator.
I first tried replacing the function with its content $$\lim_{h\to0}\dfrac{4(x+h)-13-4x-13}{h}$$ I can do this small simplification $$\lim_{h\to0}\dfrac{4(x+h)-4x-26}{h}$$ However, I do not know where to go from here
Note that you made mistake here $$\lim_{h\to0}\dfrac{4(x+h)-13-4x-\color{red}{13}}{h}$$ it should be $$\lim_{h\to0}\dfrac{4(x+h)-13-4x\color{red}{+13}}{h}$$
Given $f(x)=4x-13$ $$\lim_{h\to0}\dfrac{f(x+h)-f(x)}{h}$$ $$\lim_{h\to0}\frac{4(x+h)-13-4x+13}{h}$$ $$\lim_{h\to0}\frac{4x+4h-4x}{h}$$ $$\lim_{h\to0}\frac{4h}{h}$$ $$=4$$