Advertisements
Advertisements
प्रश्न
Evaluate the following:
`lim_(x->0) (sin^2 3x)/x^2`
Advertisements
उत्तर
`lim_(x->0) (sin^2 3x)/x^2`
`= lim_(x->0) (sin 3x)/x xx (sin 3x)/x`
`= lim_(x->0) (3 sin 3x)/(3x) xx (3 sin 3x)/(3x)`
`= 3xx3 lim_(x->0) (sin 3x)/(3x) xx lim_(x->0) (sin 3x)/(3x)`
= 9 × 1 = 9
APPEARS IN
संबंधित प्रश्न
Evaluate the following:
`lim_(x->0) (sqrt(1+x) - sqrt(1-x))/x`
Evaluate the following:
`lim_(x->a) (x^(5/8) - a^(5/8))/(x^(2/3) - a^(2/3))`
If `lim_(x->2) (x^n - 2^n)/(x-2) = 448`, then find the least positive integer n.
If f(x) = `(x^7 - 128)/(x^5 - 32)`, then find `lim_(x-> 2)` f(x)
Let f(x) = `("a"x + "b")/("x + 1")`, if `lim_(x->0) f(x) = 2` and `lim_(x->∞) f(x) = 1`, then show that f(-2) = 0
Examine the following function for continuity at the indicated point.
f(x) = `{((x^2 - 9)/(x-3) "," if x ≠ 3),(6 "," if x = 3):}` at x = 3
Find the derivative of the following function from the first principle.
ex
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)` =
