Advertisements
Advertisements
प्रश्न
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0)[(5^x + 3^x - 2^x - 1)/x]`
Evaluate the following: `lim_(x -> 0)[(log(3 - x) - log(3 + x))/x]`
Evaluate the following: `lim_(x -> 0)[(15^x - 5^x - 3^x +1)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)[(x(6^x - 3^x))/((2^x - 1)*log(1 + x))]`
Evaluate the following Limits: `lim_(x -> 0)[((5^x - 1)^2)/(x*log(1 + x))]`
Evaluate the following Limits: `lim_(x -> 0)[(log 100 + log (0.01 + x))/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) [(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)[(2^x - 1)^3/((3^x - 1)*sinx*log(1 + x))]`
Evaluate the following limit :
`lim_(x -> 0) [((49)^x - 2(35)^x + (25)^x)/(sinx* log(1 + 2x))]`
Select the correct answer from the given alternatives.
`lim_(x -> 0) ((15^x - 3^x - 5^x + 1)/sin^2x)` =
Select the correct answer from the given alternatives.
`lim_(x -> pi/2) ((3^(cosx) - 1)/(pi/2 - x))` =
Evaluate the following :
`lim_(x -> 2) [(logx - log2)/(x - 2)]`
Evaluate the following :
`lim_(x -> 1) [("ab"^x - "a"^x"b")/(x^2 - 1)]`
The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______
If f: R → R is defined by f(x) = [x - 2] + |x - 5| for x ∈ R, then `lim_{x→2^-} f(x)` is equal to ______
lf the function f(x) satisfies `lim_{x→1}(2f(x) - 5)/(2(x^2 - 1)) = e`, then `lim_{x→1}f(x)` is ______
Evaluate the following:
`lim_(x->0)[((25)^x - 2(5)^x + 1)/x^2]`
