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Calvin Khor
Calvin Khor
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I encountered this exercise: Let $f(x)$ be a differentiable function such at the point, and suppose that there exists some $a$ such aswhere $f'(a) \ne 0 $. Calculate the limit:

$$ \lim_{h\rightarrow0}\frac{f(a+3h)-f(a-2h)}{f(a-5h)-f(a-h)} $$$$ \lim_{h\rightarrow0}\frac{f(a+3h)-f(a-2h)}{f(a-5h)-f(a-h)}. $$

I have no clue how I can solve this. I was trying to separate into 2two terms, and multiply and divide by h$h$, but it solves just the numerator limit. What can be done with the denominator limit?

I encountered this exercise: Let $f(x)$ be differentiable function such at the point $a$ such as $f'(a) \ne 0 $. Calculate the limit:

$$ \lim_{h\rightarrow0}\frac{f(a+3h)-f(a-2h)}{f(a-5h)-f(a-h)} $$

I have no clue how I can solve this. I was trying to separate into 2 terms, and multiply and divide by h but it solves just the numerator limit. What can be done with the denominator limit?

I encountered this exercise: Let $f(x)$ be a differentiable function, and suppose that there exists some $a$ where $f'(a) \ne 0 $. Calculate the limit:

$$ \lim_{h\rightarrow0}\frac{f(a+3h)-f(a-2h)}{f(a-5h)-f(a-h)}. $$

I have no clue how I can solve this. I was trying to separate into two terms, and multiply and divide by $h$, but it solves just the numerator limit. What can be done with the denominator limit?

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Igor
Igor
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Limit calculation using derivative

I encountered this exercise: Let $f(x)$ be differentiable function such at the point $a$ such as $f'(a) \ne 0 $. Calculate the limit:

$$ \lim_{h\rightarrow0}\frac{f(a+3h)-f(a-2h)}{f(a-5h)-f(a-h)} $$

I have no clue how I can solve this. I was trying to separate into 2 terms, and multiply and divide by h but it solves just the numerator limit. What can be done with the denominator limit?