Let f (x) = (1 /√ 18-x2), ten value o f limx → 3 ( (f(x)-f(3) /x-3))

Question

Let f (x) = (1 /√ 18-x2), ten value o f limx → 3 ( (f(x)-f(3) /x-3))  (A) 0 (B) - (1 /9) (C) - (1 /3) (D)  (1 /9)

Tardigrade Admin · Accepted Answer

lim x→ 3 ((18 -x2)-(1/2) - ((1/3))/x-3) = lim x→ 3 (3 -√18 -x2/3(x-3) √18 -x2 ) = lim x→ 3 [(9-(18 -x2)/3(x-3) √18 -x2(3+√18 -x2))] = lim x→ 3 (x 2 -9/3(x-3) √18 -x2 [3+√18 -x2]) = lim x→ 3 (x+3/3√18-x2 [3+√18 -x2] ) = (6/3(3)(3+3)) =(1/9)

Q. Let f (x) = $\frac{1}{18 - x ^{2}}$ , ten value o f $lim_{x \to 3} (\frac{f ( x ) - f ( 3 )}{x - 3})$

0

$- \frac{1}{9}$

$- \frac{1}{3}$

$\frac{1}{9}$

Q. Let f (x) = 18−x2​1​, ten value o f limx→3​(x−3f(x)−f(3)​)

0

−91​

−31​

91​

limx→3​x−3(18−x2)−21​−(31​)​=limx→3​3(x−3)18−x2​3−18−x2​​ = limx→3​[3(x−3)18−x2​(3+18−x2​)9−(18−x2)​] = limx→3​3(x−3)18−x2​[3+18−x2​]x2−9​ = limx→3​318−x2​[3+18−x2​]x+3​ = 3(3)(3+3)6​=91​

Q. Let f (x) = $\frac{1}{18 - x ^{2}}$ , ten value o f $lim_{x \to 3} (\frac{f ( x ) - f ( 3 )}{x - 3})$

$- \frac{1}{9}$

$- \frac{1}{3}$

$\frac{1}{9}$