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# Find the limit of $\frac{\sqrt{z+6}-4}{z-10}$ as $z$ approaches $10$

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$\frac{1}{8}$$\,\,\left(\approx 0.125\right) Got another answer? Verify it here ## Step-by-step Solution Problem to solve: \lim_{z\to10}\left(\frac{\sqrt{z+6}-4}{z-10}\right) Choose the solving method 1 Applying rationalisation \lim_{z\to10}\left(\frac{\sqrt{z+6}-4}{z-10}\frac{\sqrt{z+6}+4}{\sqrt{z+6}+4}\right) Learn how to solve limits problems step by step online. \lim_{z\to10}\left(\frac{\sqrt{z+6}-4}{z-10}\frac{\sqrt{z+6}+4}{\sqrt{z+6}+4}\right) Learn how to solve limits problems step by step online. Find the limit of ((z+6)^0.5-4)/(z-10) as z approaches 10. Applying rationalisation. Multiplying fractions \frac{\sqrt{z+6}-4}{z-10} \times \frac{\sqrt{z+6}+4}{\sqrt{z+6}+4}. Solve the product of difference of squares \left(\sqrt{z+6}-4\right)\left(\sqrt{z+6}+4\right). Expand and simplify -10+z. ## Final Answer \frac{1}{8}$$\,\,\left(\approx 0.125\right)$
SnapXam A2

### beta Got another answer? Verify it!

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◻/◻
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\lim_{z\to10}\left(\frac{\sqrt{z+6}-4}{z-10}\right)$