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jek_recluse [69]

2 years ago

5

Using L'Hopital's rule, evaluate the limit as x approaches infinity of (sin (8x))/(5x)

1 answer:

sweet-ann [11.9K]2 years ago

6 0

Answer:

45.89

Step-by-step explanation:

This is what is the answer

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Find the linear approximation of the function g(x) = 3 root 1 + x at a = 0. g(x). Use it to approximate the numbers 3 root 0.95

Virty [35]

Answer:

$L(x)=1+\dfrac{1}{3}x$

$\sqrt[3]{0.95} \approx 0.9833$

$\sqrt[3]{1.1} \approx 1.0333$

Step-by-step explanation:

Given the function: $g(x)=\sqrt[3]{1+x}$

We are to determine the linear approximation of the function g(x) at a = 0.

Linear Approximating Polynomial, $L(x)=f(a)+f'(a)(x-a)$

a=0

$g(0)=\sqrt[3]{1+0}=1$

$g'(x)=\frac{1}{3}(1+x)^{-2/3} \\g'(0)=\frac{1}{3}(1+0)^{-2/3}=\frac{1}{3}$

Therefore:

$L(x)=1+\frac{1}{3}(x-0)\\\\$The linear approximating polynomial of g(x) is:$\\\\L(x)=1+\dfrac{1}{3}x$

(b) $\sqrt[3]{0.95}= \sqrt[3]{1-0.05}$

When x = - 0.05

$L(-0.05)=1+\dfrac{1}{3}(-0.05)=0.9833$

$\sqrt[3]{0.95} \approx 0.9833$

(c)

(b) $\sqrt[3]{1.1}= \sqrt[3]{1+0.1}$

When x = 0.1

$L(1.1)=1+\dfrac{1}{3}(0.1)=1.0333$

$\sqrt[3]{1.1} \approx 1.0333$

7 0

2 years ago

sasho [114]

Answer:

$y = \frac{3}{4} x - \frac{3}{2}$

Step-by-step explanation:

$y = \frac{3}{4} x - 1→y - y1 = m( x - x1)$

$y - 6 = \frac{3}{4} (x - 6)→y - 6 = \frac{3}{4} x - 6$

$2(y - 6) = 2( \frac{3}{4} )(x - 6)$

$2y - 6= \frac{3}{2}( x - 6)$

$2y - 6 = \frac{3}{2} x - 9$

$- 6 \: from \: both \: sides$

$2y = \frac{3}{2} x - 3$

$divede \: by \: 2 \: on \: both \: sides$

$y = \frac{3}{4} x - \frac{3}{2}$

Hope this helps!

7 0

3 years ago

The number 430,290,100 in expenden form

Bond [772]

Answer:

400,000,000+30,000,000+200,000+90,000+100

3 0

3 years ago

What is 10% of $34.50

ladessa [460]

Answer:

3.45

Step-by-step explanation:

3 0

2 years ago

A store sells 4 T-shirts for $38.64. What is the unit cost per T-shirt?

myrzilka [38]

The cost per shirt is $9.66 because you divide 38.64 by 4.

4 0

2 years ago

Read 2 more answers