Advertisements
Advertisements
Question
Evaluate the following: `lim_(x -> 0)[(15^x - 5^x - 3^x +1)/x^2]`
Advertisements
Solution
`lim_(x -> 0)[(15^x - 5^x - 3^x +1)/x^2]`
= `lim_(x -> 0) (5^x*3^x - 5^x - 3^x + 1)/x^2`
= `lim_(x -> 0) (5^x (3^x- 1) - 1(3^x - 1))/x^2`
= `lim_(x -> 0) ((3^x - 1) (5^x - 1))/x^2`
= `lim_(x -> 0) ((3^x - 1)/x xx (5^x - 1)/x)`
= `lim_(x -> 0) (3^x - 1)/x xx lim_(x -> 0)(5^x - 1)/x`
= `log 3* log 5 ...[lim_(x -> 0) ("a"^x - 1)/x = log"a"]`
APPEARS IN
RELATED QUESTIONS
Evaluate the following: `lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following: `lim_(x -> 0) [(2^x - 1)^2/((3^x - 1) xx log (1 + x))]`
Evaluate the following:
`lim_(x ->0)[((25)^x - 2(5)^x + 1)/x^2]`
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
Evaluate the following Limits: `lim_(x -> 0) ("e"^x + e^(-x) - 2)/x^2`
Evaluate the following Limits: `lim_(x -> 0)[((5^x - 1)^2)/(x*log(1 + x))]`
Evaluate the following limit :
`lim_(x -> 0) [(5^x + 3^x - 2^x - 1)/x]`
Evaluate the following limit :
`lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0) [(log(3 - x) - log(3 + x))/x]`
Evaluate the following limit :
`lim_(x -> 0) [(5 + 7x)/(5 - 3x)]^(1/(3x))`
Evaluate the following :
`lim_(x -> 1) [("ab"^x - "a"^x"b")/(x^2 - 1)]`
If the function
f(x) = `(("e"^"kx" - 1)tan "kx")/"4x"^2, x ne 0`
= 16 , x = 0
is continuous at x = 0, then k = ?
`lim_(x -> 0) (sin^4 3x)/x^4` = ________.
The value of `lim_{x→0} (1 + sinx - cosx + log_e(1 - x))/x^3` is ______
The value of `lim_{x→2} (e^{3x - 6} - 1)/(sin(2 - x))` is ______
`lim_(x -> 0) (15^x - 3^x - 5^x + 1)/(xtanx)` is equal to ______.
Evaluate the following:
`lim_(x->0)[((25)^x-2(5)^x+1)/x^2]`
Evaluate the following:
`lim_(x->0) [((25)^x - 2(5)^x + 1)/x^2]`
