Question

lim x tends to 7 [x^3-343/√x-√7]​

Answer 1

Step-by-step explanation:

Enter a problem...

Calculus Examples

Popular Problems Calculus Evaluate ( limit as x approaches -7 of x^3+343)/(x+7)

lim

x

→

−

7

x

3

+

343

x

+

7

limx→-7⁡x3+343x+7

Evaluate the limit of the numerator and the limit of the denominator.

Tap for more steps...

0

0

00

Since

0

0

00 is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.

lim

x

→

−

7

x

3

+

343

x

+

7

=

lim

x

→

−

7

d

d

x

[

x

3

+

343

]

d

d

x

[

x

+

7

]

limx→-7⁡x3+343x+7=limx→-7⁡ddx[x3+343]ddx[x+7]

Find the derivative of the numerator and denominator.

Tap for more steps...

lim

x

→

−

7

3

x

2

1

limx→-7⁡3x21

Take the limit of each term.

Tap for more steps...

3

(

lim

x

→

−

7

x

)

2

lim

x

→

−

7

1

3(limx→-7⁡x)2limx→-7⁡1

Evaluate the limits by plugging in

−

7

-7 for all occurrences of

x

x.

3

(

−

7

)

2

1

3(-7)21

Simplify the answer

147

147

Answer 2

Step-by-step explanation:

We have,

$\lim_{x \to 0} \dfrac{x^3-343}{\sqrt{x}-\sqrt{7}}$

To find, the value of $\lim_{x \to 0} \dfrac{x^3-343}{\sqrt{x}-\sqrt{7}}$ = ?

∴ $\lim_{x \to 0} \dfrac{x^3-343}{\sqrt{x}-\sqrt{7}}$

= $\lim_{x \to 0} \dfrac{x^3-343}{x^{\dfrac{1}{2} }-7^{\dfrac{1}{2} } }$

Dividing numerator and denominator by (x - 7), we get

$=\lim_{x \to 0} \dfrac{\dfrac{x^3-343}{x-7} }{\dfrac{x^{\dfrac{1}{2} }-7^{\dfrac{1}{2}}{x-7}}}$