The value of k so that the function f(x) = begincases (x4-256/x-4), textif x ≠ 4 [2ex] k, textif x=4 endcases is continuous at x = 4 is

Question

The value of k so that the function f(x) = begincases (x4-256/x-4), textif x ≠ 4 [2ex] k, textif x=4 endcases is continuous at x = 4 is (A) 128 (B) 64 (C) 256 (D) None of these

Tardigrade Admin · Accepted Answer

f(x) is continuous at x=4 ⇒ f(4)= displaystyle lim x arrow 4 (x4-256/x-4) = displaystyle lim x arrow 4 (x4-44/x-4)=4 ⋅ 44-1=256

Q. The value of $k$ so that the function $f (x) = ⎩ ⎨ ⎧ \frac{x ^{4} - 256}{x - 4}, k, if x \neq = 4 if x = 4$
is continuous at $x = 4$ is

128

64

256

None of these

$f (x)$ is continuous at $x = 4$
$\Rightarrow f (4) = x \to 4 lim \frac{x ^{4} - 256}{x - 4}$
$= x \to 4 lim \frac{x ^{4} - 4 ^{4}}{x - 4} = 4 \cdot 4^{4 - 1} = 256$

Q. The value of k so that the function f(x)=⎩⎨⎧​x−4x4−256​,k,​if x=4 if x=4 ​ is continuous at x=4 is

128

64

256

None of these

f(x) is continuous at x=4 ⇒f(4)=x→4lim​x−4x4−256​ =x→4lim​x−4x4−44​=4⋅44−1=256

Q. The value of $k$ so that the function $f (x) = ⎩ ⎨ ⎧ \frac{x ^{4} - 256}{x - 4}, k, if x \neq = 4 if x = 4$
is continuous at $x = 4$ is

$f (x)$ is continuous at $x = 4$
$\Rightarrow f (4) = x \to 4 lim \frac{x ^{4} - 256}{x - 4}$
$= x \to 4 lim \frac{x ^{4} - 4 ^{4}}{x - 4} = 4 \cdot 4^{4 - 1} = 256$