Advertisements
Advertisements
प्रश्न
If f(x) = `(x^7 - 128)/(x^5 - 32)`, then find `lim_(x-> 2)` f(x)
उत्तर
`lim_(x-> 2)` f(x)
= `lim_(x-> 2) (x^7 - 128)/(x^5 - 32)`
= `lim_(x-> 2) (x^7 - 2^7)/(x^5 - 2^5)`
= `(lim_(x-> 2) (x^7 - 2^7)/(x-2))/(lim_(x-> 2)(x^5 - 2^5)/(x-2))` ....[Divide both numerator amd denominator by x - 2]
`= (7 * 2^6)/(5 * 2^4)` ....`[lim_(x->"a") (x^n - "a"^n)/(x - a)]`
`= 7/5 xx 2^2 = 28/5`
APPEARS IN
संबंधित प्रश्न
Evaluate the following:
`lim_(x->0) (sqrt(1+x) - sqrt(1-x))/x`
Evaluate the following:
`lim_(x->0) (sin^2 3x)/x^2`
If `lim_(x->2) (x^n - 2^n)/(x-2) = 448`, then find the least positive integer n.
Find the derivative of the following function from the first principle.
ex
If f(x)= `{((x - |x|)/x if x ≠ 0),(2 if x = 0):}` then show that `lim_(x->1)`f(x) does not exist.
Verify the continuity and differentiability of f(x) = `{(1 - x if x < 1),((1 - x)(2 - x) if 1 <= x <= 2),(3 - x if x > 2):}` at x = 1 and x = 2.
If f(x) = `{(x^2 - 4x if x >= 2),(x+2 if x < 2):}`, then f(0) is
A function f(x) is continuous at x = a `lim_(x->"a")`f(x) is equal to:
If y = x and z = `1/x` then `"dy"/"dx"` =
`"d"/"dx" ("a"^x)` =
