Balbharati solutions for Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board chapter 7 - Limits [Latest edition]

Evaluate the following limit:

`lim_(x -> 3) [sqrt(x + 6)/x]`

Evaluate the following limits: `lim_(x -> 2)[(x^(-3) - 2^(-3))/(x - 2)]`

Evaluate the following limit:

`lim_(x -> 5)[(x^3 - 125)/(x^5 - 3125)]`

Evaluate the following limits: if `lim_(x -> 1)[(x^4 - 1)/(x - 1)] = lim_(x -> "a") [(x^3 - "a"^3)/(x - "a")]`, find all the value of a.

Evaluate the following limit:

`lim_(x -> 7)[((root(3)(x) - root(3)(7))(root(3)(x) + root(3)(7)))/(x - 7)]`

Evaluate the following limits: if `lim_(x -> 5)[(x^"k" - 5^"k")/(x - 5)]` = 500, find all possible values of k.

Evaluate the following limits: `lim_(x -> 0)[((1 - x)^8 - 1)/((1 - x)^2 - 1)]`

Evaluate the following limits: `lim_(x -> 0)[(root(3)(1 + x) - sqrt(1 + x))/x]`

Evaluate the following limits: `lim_(y -> 1) [(2y - 2)/(root(3)(7 + y) - 2)]`

Evaluate the following limits: `lim_(x -> "a")[((z + 2)^(3/2) - ("a" + 2)^(3/2))/(z - "a")]`

Evaluate the following limits: `lim_(x -> 5)[(x^3 - 125)/(x^2 - 25)]`

Evaluate the following limits: `lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`

Evaluate the following limits: `lim_(x -> - 3)[(x + 3)/(x^2 + 4x + 3)]` 

Evaluate the following limits: `lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`

Evaluate the following limits: `lim_(x -> -2)[(-2x - 4)/(x^3 + 2x^2)]`

Evaluate the following limits: `lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`

Evaluate the following limits: `lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`

Evaluate the following limits: `lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`

Evaluate the following limit:

`lim_(x -> - 2)[(x^7 + x^5 + 160)/(x^3 + 8)]`

Evaluate the following limits: `lim_(y -> 1/2)[(1 - 8y^3)/(y - 4y^3)]`

Evaluate the following limits: `lim_("v" -> sqrt(2))[("v"^2 + "v"sqrt(2) - 4)/("v"^2 - 3"v"sqrt(2) + 4)]`

Evaluate the following limits: `lim_(x -> 3)[(x^2 + 2x - 15)/(x^2 - 5x + 6)]`

Evaluate the following limits: `lim_(x -> 0) [(sqrt(6 + x + x^2) - sqrt(6))/x]`

Evaluate the following limits: `lim_(y -> 0) [(sqrt(1 - y^2) - sqrt(1 + y^2))/y^2]`

Evaluate the following limits: `lim_(x -> 2)[(sqrt(2 + x) - sqrt(6 - x))/(sqrt(x) - sqrt(2))]`

Evaluate the following limits: `lim_(x -> "a") [(sqrt("a" + 2x) - sqrt(3x))/(sqrt(3"a" + x) - 2sqrt(x))]`

Evaluate the following limits: `lim_(x -> 2)[(x^2 - 4)/(sqrt(x + 2) - sqrt(3x - 2))]`

Evaluate the following limits: `lim_(x -> 1) [(x^2 + xsqrt(x) - 2)/(x - 1)]`

Evaluate the following limits:  `lim_(x -> 0)[(sqrt(1 + x^2) - sqrt(1 + x))/(sqrt(1 + x^3) - sqrt(1 + x))]`

``Evaluate the following limits: `lim_(x -> 4) [(x^2 + x - 20)/(sqrt(3x + 4) - 4)]`

Evaluate the following limits: `lim_(x -> 2) [(x^3 - 8)/(sqrt(x + 2) - sqrt(3x - 2))]`

Evaluate the following limits: `lim_(y -> 2) [(2 - y)/(sqrt(3 - y) - 1)]`

Evaluate the following limits: `lim_(z -> 4) [(3 - sqrt(5 + z))/(1 - sqrt(5 - z))]`

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) [(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)[(log(3 - x) - log(3 + x))/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 -> 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: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`

if `lim_(x -> 2) (x^"n"- 2^"n")/(x - 2)` = 80 then find the value of n.

Evaluate the following Limits: `lim_(x -> "a") ((x + 2)^(5/3) - ("a" + 2)^(5/3))/(x - "a")`

Evaluate the following Limit:

`lim_(x -> 0) ((1 + x)^"n" - 1)/x`

Evaluate the following Limits: `lim_(x -> 2)[((x - 2))/(2x^2 - 7x + 6)]`

Evaluate the following limit:

`lim_(x -> 1)[(x^3 - 1)/(x^2 + 5x - 6)]`

Evaluate the following Limits: `lim_(x -> 3)[(x - 3)/(sqrt(x - 2) - sqrt(4 - x))]`

Evaluate the following Limits: `lim_(x -> 4)[(3 - sqrt(5 + x))/(1 - sqrt(5 - x))]`

Evaluate the following Limits: `lim_(x -> 0)[(5^x - 1)/x]`

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 Limits: `lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/x]`

Evaluate the following Limits: `lim_(x -> 0) ("e"^x + e^(-x) - 2)/x^2`

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)[("a"^(3x) - "a"^(2x) - "a"^x  + 1)/x^2]`

Evaluate the following Limits: `lim_(x -> 0)[((5^x - 1)^2)/(x*log(1 + x))]`

Evaluate the following Limits: `lim_(x -> 0) [("a"^(4x) - 1)/("b"^(2x) - 1)]`

Evaluate the following Limits: `lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`

Evaluate the following Limits: `lim_(x -> 0)[(log(4 - x) - log(4 + x))/x]`

Evaluate the limit of the function if exist at x = 1 where, f(x) = `{(7 - 4x, x < 1),(x^2 + 2, x ≥ 1):}`