F-x-4x-1-3sin-xp-log-1-x23-is continous x-0 and f-0-12-log4-3 then p- -

Solve

Guides

Standard X

Mathematics

Trigonometric Ratios

Question

$f (x) = \frac{{(4^{x} - 1)}^{3}}{s i n (\frac{x}{p}) l o g (1 + \frac{x^{2}}{3})}$ is continous at x=0 and f(0)=12 ${(l o g 4)}^{3}$ then p= __________.

Open in App

Solution

Verified by Toppr

Was this answer helpful?

Similar Questions

Determine f(0) so that the function f(x) defined by f(x) = (4x-1)³ / [sinx/4 log(1+x²/3) becomes continuous at x=0.

View Solution

If $f (x) = x + | x | + cos ([π^{2}] x)$ and $g (x) = sin x,$ then which of the following option is INCORRECT ?

(where [.] denotes the greatest integer function)

View Solution

The value of p for which the function

f (x) = \frac{(4^{x} - 1)^{3}}{s i n (\frac{x}{p}) l n (1 + \frac{x^{2}}{3})}, x \neq 0 = 12 (l n 4)^{3}, x = 0

may be continuous at x = 0 is

View Solution

If $f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{(4^{x} - 1)^{3}}{sin (\frac{x}{a}) ln (1 + \frac{x^{2}}{3})}, & x \neq 0 9 (ln 4)^{3}, & x = 0 \end{matrix}$ is continuous at $x = 0$ , then the value of $a$ is

View Solution

If $f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \begin{matrix} \frac{{(4^{x} - 1)}^{3}}{sin (\frac{x}{a}) log [1 + (\frac{x^{2}}{3})]}, & x \neq 0 \end{matrix} \begin{matrix} 9 {(log 4)}^{3}, & x = 0 \end{matrix} \end{matrix}$ is a continuous function at $x = 0$ , then the value of $a$ is equal to

View Solution

Solve

Guides

f(x)=(4x−1)3sin(xp)log(1+x23)is continous at x=0 and f(0)=12(log4)3 then p= __________.

$f (x) = \frac{{(4^{x} - 1)}^{3}}{s i n (\frac{x}{p}) l o g (1 + \frac{x^{2}}{3})}$ is continous at x=0 and f(0)=12 ${(l o g 4)}^{3}$ then p= __________.