Advertisements
Advertisements
प्रश्न
Evaluate the following limit :
`lim_(x -> 0) [(5^x + 3^x - 2^x - 1)/x]`
उत्तर
`lim_(x -> 0) [(5^x + 3^x - 2^x - 1)/x]`
= `lim_(x -> 0) [((5^x - 1) + (3^x - 1) - (2^x - 1))/x]`
= `lim_(x -> 0) [(5^x - 1)/x + (3^x - 1)/x - (2^x - 1)/x]`
= `lim_(x -> 0) (5^x - 1)/x + lim_(x -> 0) (3^x - 1)/x - lim_(x -> 0) (2^x - 1)/x`
= log 5 + log 3 – log 2 ...`[because lim_(x -> 0) ("a"^x - 1)/x = log"a"]`
= `log((5 xx 3)/2)`
= `log(15/2)`
APPEARS IN
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0) [(3^x + 3^-x - 2)/x^2]`
Evaluate the following: `lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following: `lim_(x -> 0) [("a"^(3x) - "b"^(2x))/(log 1 + 4x)]`
Evaluate the following: `lim_(x -> 0) [(2^x - 1)^2/((3^x - 1) xx log (1 + 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)[("a"^x + "b"^x + "c"^x - 3)/x]`
Evaluate the following Limits: `lim_(x -> 0) ("e"^x + e^(-x) - 2)/x^2`
Evaluate the following Limits: `lim_(x -> 0)[("a"^(3x) - "a"^(2x) - "a"^x + 1)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)[((5^x - 1)^2)/(x*log(1 + x))]`
Evaluate the following Limits: `lim_(x -> 0) [("a"^(4x) - 1)/("b"^(2x) - 1)]`
Evaluate the following limit :
`lim_(x -> 0) [(9^x - 5^x)/(4^x - 1)]`
Evaluate the following limit :
`lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0) [(5 + 7x)/(5 - 3x)]^(1/(3x))`
Evaluate the following limit :
`lim_(x -> 0)[(15^x - 5^x - 3^x + 1)/(x*sinx)]`
Evaluate the following limit :
`lim_(x -> 0) [((25)^x - 2(5)^x + 1)/(x*sinx)]`
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) ((3 + 5x)/(3 - 4x))^(1/x)` =
Select the correct answer from the given alternatives.
`lim_(x -> 0) [(x*log(1 + 3x))/("e"^(3x) - 1)^2]` =
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)[("e"^x + "e"^-x - 2)/(x*tanx)]`
Evaluate the following :
`lim_(x -> 0) [("a"^(3x) - "a"^(2x) - "a"^x + 1)/(x*tanx)]`
Evaluate the following :
`lim_(x -> 2) [(logx - log2)/(x - 2)]`
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 = ?
The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______
lf the function f(x) satisfies `lim_{x→1}(2f(x) - 5)/(2(x^2 - 1)) = e`, then `lim_{x→1}f(x)` is ______
`lim_(x -> 0) (sin^4 3x)/x^4` = ________.
`lim_(x -> 0) (15^x - 3^x - 5^x + 1)/(xtanx)` is equal to ______.
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]`
Evaluate the following:
`lim_(x->0)[((25)^x -2(5)^x +1)/(x^2)]`
