Advertisements
Advertisements
प्रश्न
Evaluate the following: `lim_(x -> 0)[(log(2 + x) - log( 2 - x))/x]`
Advertisements
उत्तर
`lim_(x -> 0)[(log(2 + x) - log( 2 - x))/x]`
= `lim_(x -> 0)(log[2(1 + x/2)] - log[2(1 - x/2)])/x`
= `lim_(x -> 0) (log2 + log(1 + x/2) - [log2 + log(1 - x/2)])/x`
= `lim_(x -> 0) (log(1 + x/2) - log(1 - x/2))/x`
= `lim_(x -> 0) [(log(1 + x/2))/x - (log(1 - x/2))/x]`
= `lim_(x -> 0) [(log(1 + x/2))/(2(x/2)) - (log(1 - x/2))/((-2)(-x/2))]`
= `1/2 lim_(x -> 0) (log(1 + x/2))/(x/2) + 1/2 lim_(x -> 0) (log(1 - x/2))/(-x/2)`
= `1/2(1) + 1/2(1) ....[(because x -> 0"," x/2 -> 0 and),(lim_(x -> 0) (log(1 + x))/x = 1)]`
= 1
APPEARS IN
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0)[(5^x + 3^x - 2^x - 1)/x]`
Evaluate the following: `lim_(x -> 0) [(2^x - 1)^2/((3^x - 1) xx log (1 + x))]`
Evaluate the following: `lim_(x -> 0)[(15^x - 5^x - 3^x +1)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)(1 + x/5)^(1/x)`
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) [(9^x - 5^x)/(4^x - 1)]`
Evaluate the following limit :
`lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/sinx]`
Evaluate the following limit :
`lim_(x -> 0) [(8^sinx - 2^tanx)/("e"^(2x) - 1)]`
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 -> pi/2) ((3^(cosx) - 1)/(pi/2 - x))` =
Evaluate the following :
`lim_(x -> 0) [((5^x - 1)^2)/((2^x - 1)log(1 + x))]`
The value of `lim_{x→0}{(a^x + b^x + c^x + d^x)/4}^{1/x}` is ______
The value of `lim_{x→0} (1 + sinx - cosx + log_e(1 - x))/x^3` is ______
The value of `lim_{x→2} (e^{3x - 6} - 1)/(sin(2 - x))` is ______
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]`
