Advertisements
Advertisements
प्रश्न
Evaluate the following:
`lim_(x->∞) (sum "n")/"n"^2`
Advertisements
उत्तर
`lim_(x->∞) (sum "n")/"n"^2`
= `lim_(x->∞) (("n"("n"+1))/2)/"n"^2`
= `lim_(x->∞) ("n"^2(1 + 1/"n"))/(2"n"^2)`
= `lim_(x->∞) 1/2(1 + 1/"n")`
= `1/2 (1+1/∞)`
`= 1/2`(1 + 0)
`= 1/2`
APPEARS IN
संबंधित प्रश्न
Evaluate the following:
\[\lim_{x->∞} \frac{2x + 5}{x^2 + 3x + 9}\]
Evaluate the following:
`lim_(x->0) (sqrt(1+x) - sqrt(1-x))/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
If f(x) = `{(x^2 - 4x if x >= 2),(x+2 if x < 2):}`, then f(0) is
\[\lim_{x->0} \frac{e^x - 1}{x}\]=
`"d"/"dx"` (5ex – 2 log x) is equal to:
If y = e2x then `("d"^2"y")/"dx"^2` at x = 0 is:
`"d"/"dx" ("a"^x)` =
