Advertisements
Advertisements
Question
Evaluate the following Limits: `lim_(x -> 0) [("a"^(4x) - 1)/("b"^(2x) - 1)]`
Advertisements
Solution
`lim_(x -> 0) ("a"^(4x) - 1)/("b"^(2x) - 1)`
= `lim_(x -> 0) (("a"^(4x) - 1)/x)/(("b"^(2x) - 1)/x)`
= `(lim_(x -> 0)(("a"^(4x) - 1)/(4x)) xx 4)/(lim_(x -> 0)(("b"^(2x) - 1)/(2x)) xx 2`
= `(4log"a")/(2log"b") ...[("As" x -> 0"," 2x -> 0"," 4x -> 0),(and lim_(x -> 0) ("a"^x - 1)/x = log "a")]`
= `(2log"a")/(log "b")`
APPEARS IN
RELATED QUESTIONS
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)[(log(2 + x) - log( 2 - x))/x]`
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)[((25)^x - 2(5)^x + 1)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)[(log(1 + 9x))/x]`
Evaluate the following Limits: `lim_(x -> 0)((1 - x)^5 - 1)/((1 - x)^3 - 1)`
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) [(8^sinx - 2^tanx)/("e"^(2x) - 1)]`
Evaluate the following limit :
`lim_(x -> 0) [(3^x + 3^-x - 2)/(x*tanx)]`
Evaluate the following limit :
`lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0) [((25)^x - 2(5)^x + 1)/(x*sinx)]`
Evaluate the following :
`lim_(x -> 0) [("a"^(3x) - "a"^(2x) - "a"^x + 1)/(x*tanx)]`
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 ______
The value of `lim_{x→0} (1 + sinx - cosx + log_e(1 - x))/x^3` is ______
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]`
