Advertisements
Advertisements
प्रश्न
Evaluate the following limit :
`lim_(x -> 0) [((49)^x - 2(35)^x + (25)^x)/(sinx* log(1 + 2x))]`
Advertisements
उत्तर
`lim_(x -> 0) [((49)^x - 2(35)^x + (25)^x)/(sinx* log(1 + 2x))]`
= `lim_(x -> 0) ((7^x)^2 - 2(7^x) (5^x) + (5^x)^2)/(sinx log (1 + 2x)) ...[(35^x = (5*7)^x = 5^x * 7^x),(49^x = (7^2)x = (7^x)^2)]`
= `lim_(x -> 0) [7^x - 5^x]^2/(sinx log (1 + 2x)`
= `lim_(x -> 0) [(7^x - 1) - (5^x- 1)]^2/(sin x log (1 + 2x))`
= `lim_(x -> 0) [(7^x - 1)/x - (5^x - 1)/x]^2/([sinx/x][(log(1 + 2x))/x])` ...[∵ x → 0, ∴ x ≠ 0]
= `([lim_(x -> 0) ((7^x - 1)/x - (5^x - 1)/x)]^2)/([lim_(x -> 0) sinx/x] xx 2 [lim_(x -> 0) (log(1 + 2x))/(2x)]`
= `[log 7 - log 5]^2/([1] xx 2[1]) ...[because x -> 0 "," 2x -> 0 "and" lim_(x -> 0) (log(1 + x))/x = 1 "and" lim_(x -> 0) ("a"^x - 1)/x = log"a"]`
= `1/2[log(7/5)]^2`
APPEARS IN
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0)[(9^x - 5^x)/(4^x - 1)]`
Evaluate the following: `lim_(x -> 0)[(5^x + 3^x - 2^x - 1)/x]`
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: `lim_(x -> 2) [(3^(x/2) - 3)/(3^x - 9)]`
Evaluate the following Limits: `lim_(x -> 0)[(log(1 + 9x))/x]`
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)[(log(4 - x) - log(4 + x))/x]`
Evaluate the following limit :
`lim_(x -> 0) [(8^sinx - 2^tanx)/("e"^(2x) - 1)]`
Evaluate the following limit :
`lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0)[(5x + 3)/(3 - 2x)]^(2/x)`
Evaluate the following limit :
`lim_(x -> 0) [(log(3 - x) - log(3 + x))/x]`
Evaluate the following limit :
`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/x)`
Evaluate the following limit :
`lim_(x ->0) [("a"^x - "b"^x)/(sin(4x) - sin(2x))]`
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)]`
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 -> 0) [(x*log(1 + 3x))/("e"^(3x) - 1)^2]` =
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→∞} ((3x + 3)^40(9x - 3)^5)/(3x + 1)^45` = ______
`lim_(x -> 0) (log(1 + (5x)/2))/x` is equal to ______.
`lim_(x -> 0) (sin^4 3x)/x^4` = ________.
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 limit:
`lim_(z->2)[(z^2-5x+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]`
