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Standard Limits to Remove Indeterminate Form

Let gx=x-1n...

Question

Let $g (x) = \frac{(x - 1)^{n}}{log {cos}^{m} (x - 1)}; 0 < x < 2, m$ and $n$ are integers, $m \neq 0, n > 0$ , and let $p$ be the left hand derivative of $| x - 1 |$ at $x = 1$ . If $lim x \to 1^{+} g (x) = p$ , then

A

n = 1, m = 1

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B

n = 1, m = 3

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C

n = 2, m = 2

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D

n > 2, m = n

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Solution

The correct option is C $n = 2, m = 2$

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Similar questions

g (x) = \frac{{(x - 1)}^{n}}{log {cos}^{m} (x - 1)}; 0 < x < 2,

m and n are integers,

m \neq 0, n > 0,

and let p be the left hand derivative of

| x - 1 |

x = 1.

lim x \to 1 + g (x) = p

g (x) = \frac{{(x - 1)}^{n}}{log {cos}^{m} (x - 1)}

; 0< x< 2 and m and n are integers,

m \neq 0

, n> 0, and let p be the left hand derivative of |x-1| at x=1. If

{lim}_{x \to 1} g (x) = p

f (x) = (x - 1)^{m} (2 - x)^{n}; m, n ϵ N

m, n > 2

x, y

be positive real numbers and

m, n

positive integers. The maximum value of the expression

\frac{x^{m} y^{n}}{(1 + x^{2 m}) (1 + y^{2 n})}

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n},

n \in N,

2 \leq m \leq n,

C_{0} - C_{1} + C_{2} - \dots + [(- 1)^{m - 1}] C_{m - 1}

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