Advertisements
Advertisements
प्रश्न
Evaluate the following limit :
`lim_(x -> 0)[(15^x - 5^x - 3^x + 1)/(x*sinx)]`
Advertisements
उत्तर
`lim_(x -> 0)[(15^x - 5^x - 3^x + 1)/(xsinx)]`
= `lim_(x -> 0) (5^x * 3^x - 5^x - 3^x + 1)/(xsinx)`
= `lim_(x -> 0) (5^x (3^x - 1) - (3^x - 1))/(xsinx)`
= `lim_(x -> 0) ((3^x - 1)(5^x - 1))/(xsinx)`
= `lim_(x -> 0) (((3^x - 1)/x)((5^x - 1)/x))/((sinx/x))` ...[∵ x → 0, ∴ x ≠ 0]
= `((log3)(log5))/1 ...[because lim_(x -> 0) ("a"^x - 1)/x = log"a"]`
= (log 3) (log 5).
APPEARS IN
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0)[(log(3 - x) - log(3 + x))/x]`
Evaluate the following: `lim_(x -> 0) [("a"^(3x) - "b"^(2x))/(log 1 + 4x)]`
Evaluate the following: `lim_(x -> 0)[(15^x - 5^x - 3^x +1)/x^2]`
Evaluate the following: `lim_(x -> 2) [(3^(x/2) - 3)/(3^x - 9)]`
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)[(5^x - 1)/x]`
Evaluate the following Limits: `lim_(x -> 0)[(log(1 + 9x))/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)[(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)[(5x + 3)/(3 - 2x)]^(2/x)`
Evaluate the following limit :
`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/x)`
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 -> 1) [("ab"^x - "a"^x"b")/(x^2 - 1)]`
The value of `lim_{x→0}{(a^x + b^x + c^x + d^x)/4}^{1/x}` is ______
`lim_{x→∞} ((3x + 3)^40(9x - 3)^5)/(3x + 1)^45` = ______
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 ______
`lim_(x -> 0) (log(1 + (5x)/2))/x` is equal to ______.
Evaluate the following `lim_(x->0)[((25)^x - 2(5)^x+1) /(x^2)]`
Evaluate the following Limit.
`lim_(x->1)[(x^3-1)/(x^2+5x-6)]`
Evaluate the following :
`lim_(x -> 0) [((25)^x - 2(5)^x + 1)/x^2]`
Evaluate the following limit :
`lim(x>2)[(z^2 -5z+6)/(z^2-4)]`
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)]`
Evaluate the following:
`lim_(x->0) [((25)^x - 2(5)^x + 1)/x^2]`
