Advertisements
Advertisements
प्रश्न
Evaluate the following: `lim_(x -> 0)[(9^x - 5^x)/(4^x - 1)]`
Advertisements
उत्तर
`lim_(x -> 0)(9^x - 5^x)/(4^x - 1)`
= `lim_(x -> 0) (9^x - 1 + 1 - 5^x)/(4^x - 1)`
= `lim_(x -> 0) ((9^x - 1) - (5^x - 1))/(4^x - 1)`
= `lim_(x -> 0) ((9^x - 1 - 5^x - 1)/x)/((4^x - 1)/x` ...[∵ x → 0, ∴ x ≠ 0]
= `lim_(x -> 0) (((9^x - 1)/x) - ((5^x - 1)/x))/(((4^x - 1)/x)`
= `(lim_(x -> 0) (9^x - 1)/x - lim_(x -> 0) (5^x - 1)/x)/(lim_(x -> 0) (4^x - 1)/x)`
= `(log9 - log5)/(log4) ...[because lim_(x -> 0) ("a"^x - 1)/x = log "a"]`
= `1/(log4)log(9/5)`
APPEARS IN
संबंधित प्रश्न
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)[(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 limit :
`lim_(x -> 0)[(2^x - 1)^3/((3^x - 1)*sinx*log(1 + x))]`
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 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 ______
`lim_(x -> 0) (15^x - 3^x - 5^x + 1)/(xtanx)` is equal to ______.
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 :
`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 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)]`
