SOLUTION: Kindly help me solving it i tried my best but I couldn't lim (10^x-5^x-2^x+1)/x^2 is equal to x➡0

Algebra ->  Functions -> SOLUTION: Kindly help me solving it i tried my best but I couldn't lim (10^x-5^x-2^x+1)/x^2 is equal to x➡0      Log On


   

Question 1044766: Kindly help me solving it i tried my best but I couldn't
lim (10^x-5^x-2^x+1)/x^2 is equal to
x➡0
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
lim%28x-%3E0%2C+%2810%5Ex-5%5Ex-2%5Ex%2B1%29%2Fx%5E2%29+
= lim%28x-%3E0%2C+%28ln10%2A10%5Ex-ln5%2A5%5Ex-ln2%2A2%5Ex%29%2F%282x%29%29
= .
The last expression doesn't lead to an indeterminate form and so direct substitution of x = 0 gives...
highlight%28%28%28ln10%29%5E2-%28ln5%29%5E2-%28ln2%29%5E2%29%2F2%29%29.


Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
Kindly help me solving it i tried my best but I couldn't
lim (10^x-5^x-2^x+1)/x^2 is equal to
x-->0
~~~~~~~~~~~~~~~~~~~~~ 

%2810%5Ex-5%5Ex-2%5Ex%2B1%29%2Fx%5E2 = %28%281-5%5Ex%29%2A%281-2%5Ex%29%29%2Fx%5E2 = %281-5%5Ex%29%2Fx.%281-2%5Ex%29%2Fx.

Therefore,

lim   ( (10^x-5^x-2^x+1)/x^2)  is equal to  ln(5) * ln(2).
x➡0