Advertisements
Advertisements
प्रश्न
Evaluate the following Limits: `lim_(x -> 0)[((5^x - 1)^2)/(x*log(1 + x))]`
Advertisements
उत्तर
`lim_(x -> 0)((5^x - 1)^2)/(x*log(1 + x))`
= `lim_(x -> 0) ((5^x - 1)^2/x^2)/((x*log(1 + x))/x^2) ...[("As" x -> 0"," x ≠ 0 therefore x^2 ≠ 0),("Divide Numerator and"),("Denominator by " x^2)]`
= `(lim_(x -> 0)((5^x - 1)/x)^2)/(lim_(x -> 0)(log(1 + x))/x`
= `(log 5)^2/1 ...[(lim_(x -> 0) ("a"^x - 1)/x = log "a"","),(lim_(x -> 0) (log(1 + x))/x = 1)]`
= (log 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)[((25)^x - 2(5)^x + 1)/x^2]`
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)[(x(6^x - 3^x))/((2^x - 1)*log(1 + x))]`
Evaluate the following limit :
`lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/sinx]`
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 -> pi/2) ((3^(cosx) - 1)/(pi/2 - x))` =
Evaluate the following :
`lim_(x -> 2) [(logx - log2)/(x - 2)]`
`lim_(x -> 0) (15^x - 3^x - 5^x + 1)/(xtanx)` 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:
`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)]`
