Question

Limx-0 a^x-b^x/a-b is equal to

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

taking the above equation to be

ASSUME THAT

a=x

b=y

x=n

for simplification

$\lim_{n \to 0} \frac{x^n-a^n}{x-a}$

we get

$\lim_{n \to a+} \frac{x^n-a^n}{x-a}$

solving we get

$\lim_{h \to0 } \frac{(a+h)^n-a^n}{a+h-a}$

$\lim_{h \to 0} \frac{a^n[ ((1+h/a)^n-1)}{h}$

on solving the equation further we get

$a^n \lim_{h \to 0} \frac{((1+nh/a)-1)}{h}$

where x→0

and

$(1+x)^n----> n1+nx$

on solving the above equation we get

=$a^{n} \frac{n}{a}$

which is also equal to

n$a^{n-1}$

Step-by-step explanation: