Question
Asked Sep 9, 2019

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Find the limit.
2
15 4
lim
x 1
x 1
x15 4
lim
x 1
|(Type an integer or a simplified fraction.)
x 1
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Find the limit. 2 15 4 lim x 1 x 1 x15 4 lim x 1 |(Type an integer or a simplified fraction.) x 1

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Expert Answer

Step 1

The given expression is:

Vx2 +15 - 4
lim
x1
x -1
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Vx2 +15 - 4 lim x1 x -1

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Step 2

To find the limit of function at point x=1, first rationalise the function under the limit

lim Vx +15-4
x1
x2154
2
+15 4
limVx15 -4
Vx15 4
x1
2
-42
= lim
(x-1)(v
x1
15 4
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lim Vx +15-4 x1 x2154 2 +15 4 limVx15 -4 Vx15 4 x1 2 -42 = lim (x-1)(v x1 15 4

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Step 3

Now,

...
(P15
-42
= lim
15 4
х —1
(x +15-16)
= lim
x1
15 4
(x +15-16)
= lim
x -1)(Vx-+15 + 4
(x2-1)
_
lim
x1
(x-1)
15 4
(x-1)(x+1)
= lim
'(x -1)(*
x-1
x- +15 + 4
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(P15 -42 = lim 15 4 х —1 (x +15-16) = lim x1 15 4 (x +15-16) = lim x -1)(Vx-+15 + 4 (x2-1) _ lim x1 (x-1) 15 4 (x-1)(x+1) = lim '(x -1)(* x-1 x- +15 + 4

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Math

Calculus

Limits

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