limx → 4 (3- √ 5+x /x-4)

Question

limx → 4 (3- √ 5+x /x-4)  (A) 1/2 (B) 0 (C) 3 (D) 1

Tardigrade Admin · Accepted Answer

limx→4 (3-√5+x /x-4) = limx→4 ((3-√5+x)(3+√5+x)/(x-4)(3+√5 +x) ) = limx→4 (9 - 5 -x/(x-4)(3+ √3+x)) = limx→4 (4-x/(x-4)(3+√5+x )) = (-1/3 +√5 +4) = - (1/6)

Q. $lim_{x \to 4} \frac{3 - 5 + x}{x - 4}$

1/2

0

3

1

$lim_{x \to 4} \frac{3 - 5 + x}{x - 4}$
= $lim_{x \to 4} \frac{( 3 - 5 + x ) ( 3 + 5 + x )}{( x - 4 ) ( 3 + 5 + x )}$
= $lim_{x \to 4} \frac{9 - 5 - x}{( x - 4 ) ( 3 + 3 + x )}$
= $lim_{x \to 4} \frac{4 - x}{( x - 4 ) ( 3 + 5 + x )}$
= $\frac{- 1}{3 + 5 + 4} = - \frac{1}{6}$

Q. limx→4​x−43−5+x​​

1/2

0

3

1

limx→4​x−43−5+x​​ = limx→4​(x−4)(3+5​+x)(3−5+x​)(3+5+x​)​ = limx→4​(x−4)(3+3+x​)9−5−x​ = limx→4​(x−4)(3+5+x​)4−x​ = 3+5+4​−1​=−61​

Q. $lim_{x \to 4} \frac{3 - 5 + x}{x - 4}$

$lim_{x \to 4} \frac{3 - 5 + x}{x - 4}$
= $lim_{x \to 4} \frac{( 3 - 5 + x ) ( 3 + 5 + x )}{( x - 4 ) ( 3 + 5 + x )}$
= $lim_{x \to 4} \frac{9 - 5 - x}{( x - 4 ) ( 3 + 3 + x )}$
= $lim_{x \to 4} \frac{4 - x}{( x - 4 ) ( 3 + 5 + x )}$
= $\frac{- 1}{3 + 5 + 4} = - \frac{1}{6}$