Question

If f(x) = 3x^10 -7x^8+5x^6-21x^3+3x^3-7 then
Lim f(1-a)-f(1)/a^3+3a
When a tends to 0 is

Answer 1

I want to know if we can do it some other way except for L' hospitals rule..
Bcoz it is becuming very perplexing..

Answer 2

3x^2 in the question

Answer 3

After 21x^3 term

Answer 4

You can use definition of derivative
Recall:
\[\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}=f'(x) \\ \text{ if we let } h=-a \\ \text{ then it looks like } \\ \lim_{a \rightarrow 0}\frac{f(x-a)-f(x)}{-a}=f'(x) \\\]

Answer 5

\[\lim_{a \rightarrow 0} \frac{f(1-h)-f(1)}{a(a^2+3)}=-\lim_{a \rightarrow 0} \frac{f(1-h)-f(1)}{-a} \cdot \lim_{a \rightarrow 0} \frac{1}{a^2+3}\]

Answer 6

I have said too much now :p

Answer 7

but please let me know if you need assistance