6-(-1)6. Find the local extreme values of fand the intervals on which fis increasing or is decreasing,2and sketch the graph of f (x) = x3 (8 - x).7. Find the limit or show that it does not exist H al5x2-7x+9Pule sfor practire proklems a-tVRedа. limx-oToklevms a10x2+3x-4x3-2x+4b. limx-cox2-6x-76X+12c. limx-007x2+9Ior2x2+3x-1d. limxco 3x2-x-9V4x2-9e. limx ox+33x-8f. limxo x2-6x-10Find the equations of the horizontal and vertical asymptotes of each curve.a. у 3x2-25

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Asked Nov 8, 2019
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I need help understanding how to solve letter E. Using L'Hopitals rule.

6-(-1)
6. Find the local extreme values of fand the intervals on which fis increasing or is decreasing,
2
and sketch the graph of f (x) = x3 (8 - x).
7. Find the limit or show that it does not exist H al
5x2-7x+9
Pule s
for practire proklems a-t
VRed
а. limx-o
Toklevms a
10x2+3x-4
x3-2x+4
b. limx-co
x2-6x-7
6X+12
c. limx-00
7x2+9
Ior
2x2+3x-1
d. limxco 3x2-x-9
V4x2-9
e. limx o
x+3
3x-8
f. limxo x2-6x-10
Find the equations of the horizontal and vertical asymptotes of each curve.
a. у 3
x2-25
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6-(-1) 6. Find the local extreme values of fand the intervals on which fis increasing or is decreasing, 2 and sketch the graph of f (x) = x3 (8 - x). 7. Find the limit or show that it does not exist H al 5x2-7x+9 Pule s for practire proklems a-t VRed а. limx-o Toklevms a 10x2+3x-4 x3-2x+4 b. limx-co x2-6x-7 6X+12 c. limx-00 7x2+9 Ior 2x2+3x-1 d. limxco 3x2-x-9 V4x2-9 e. limx o x+3 3x-8 f. limxo x2-6x-10 Find the equations of the horizontal and vertical asymptotes of each curve. a. у 3 x2-25

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Step 1

To use L’Hospital’s rule, differentiate the numerator and denominator separately with respect to the variable x.

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V4x2-9 dx d lim (x+3) d (4x2-9) 1 2/4x-9 d =lim d (x) (3) dx 1 ..8x 2/4x2-9 =lim x 10 4х = lim 4x29

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Step 2

The term in the numerator is taken in the denominator and under the radical sign. Hence 4x is written as 16x2 in the denominator. Simplification is done as shown,

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1 lim 4x2-9 4x 1 - lim 4x2-9 16x2 Split the denominator and simplify; 1 =lim 4x2 16x 16x2 = lim 1 x 4 16x2

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Step 3

Substitute the va...

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1 1 9 16() 4 1 Using property of o, i.e.-=0; 1 1 1 = 2

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Calculus