Advertisements
Advertisements
Question
If `lim_(x->2) (x^n - 2^n)/(x-2) = 448`, then find the least positive integer n.
Advertisements
Solution
`lim_(x->2) (x^n - 2^n)/(x-2) = 448`
i.e., n 2n-1 = 7 × 26
n × 2n-1 = 7 × 27-1
∴ n = 7
APPEARS IN
RELATED QUESTIONS
Evaluate the following:
\[\lim_{x->∞} \frac{2x + 5}{x^2 + 3x + 9}\]
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
Show that f(x) = |x| is continuous at x = 0.
Find the derivative of the following function from the first principle.
log(x + 1)
Find the derivative of the following function from the first principle.
ex
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.
`lim_(theta->0) (tan theta)/theta` =
If y = e2x then `("d"^2"y")/"dx"^2` at x = 0 is:
If y = log x then y2 =
