Advertisements
Advertisements
Question
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
Advertisements
Solution
`lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
= `lim_(x-> 0) [((7^2)^x - 2(7 xx 5)^x + (5^2)^x)/x^2]`
= `lim_(x-> 0) [((7^x)^2 - 2 * 7^x xx 5^x + (5^x)^2)/x^2]`
= `lim_(x -> 0) [(7^x - 5^x)^2/x^2]`
= `lim_(x -> 0) ((7^x - 5^x)/x)^2`
= `lim_(x -> 0) [(7^x - 1 - 5^x - 1)/x]^2`
= `lim_(x -> 0)[(7^x - 1)/x - (5^x - 1)/x]^2`
= `[lim_(x -> 0) (7^x - 1)/x - lim_(x -> 0) (5^x - 1)/x]^2`
= `(log 7 - log 5)^2 ...[lim_(x -> 0) ("a"^x - 1)/x = log"a"]`
= `(log 7/5)^2`.
APPEARS IN
RELATED QUESTIONS
Evaluate the following: `lim_(x -> 0)[(log(2 + x) - log( 2 - x))/x]`
Evaluate the following: `lim_(x -> 0)[(log(3 - x) - log(3 + x))/x]`
Evaluate the following Limits: `lim_(x -> 0)[(5^x - 1)/x]`
Evaluate the following Limits: `lim_(x -> 0)(1 + x/5)^(1/x)`
Evaluate the following Limits: `lim_(x -> 0)[(log(1 + 9x))/x]`
Evaluate the following Limits: `lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/x]`
Evaluate the following limit :
`lim_(x -> 0) [(5^x + 3^x - 2^x - 1)/x]`
Evaluate the following limit :
`lim_(x -> 0) [(6^x + 5^x + 4^x - 3^(x + 1))/sinx]`
Evaluate the following limit :
`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0) [(5 + 7x)/(5 - 3x)]^(1/(3x))`
Evaluate the following limit :
`lim_(x ->0) [("a"^x - "b"^x)/(sin(4x) - sin(2x))]`
Select the correct answer from the given alternatives.
`lim_(x -> 3) [(5^(x - 3) - 4^(x - 3))/(sin(x - 3))]` =
Evaluate the following :
`lim_(x -> 0) [((5^x - 1)^2)/((2^x - 1)log(1 + x))]`
The value of `lim_{x→0}{(a^x + b^x + c^x + d^x)/4}^{1/x}` is ______
Evaluate the following limit :
`lim_(x->0)[(sqrt(6+x+x^2)-sqrt6)/x]`
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]`
Evaluate the following:
`lim_(x->0)[((25)^x - 2(5)^x + 1)/x^2]`
