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3 years ago

Find the derivative of f(x) = 6x + 2 at x = 1.

2 answers:

6 0

$f'(x_0)=\lim\limits_{x\to x_0}\dfrac{f(x)-f(x_0)}{x-x_0}\\\\f(x)=6x+2;\ x_0=1\\\\f'(1)=\lim\limits_{x\to x_0}\dfrac{(6x+2)-(6\cdot1+2)}{x-1}=\lim\limits_{x\to x_0}\dfrac{6x+2-8}{x-1}\\\\=\lim\limits_{x\to x_0}\dfrac{6x-6}{x-1}=\lim\limits_{x\to x_0}\dfrac{6(x-1)}{x-1}=\lim\limits_{x\to x_0}6=6\\\\\\Answer:\boxed{f'(1)=6}$

alexandr1967 [171]3 years ago

5 0

Answer:

Step-by-step explanation:

Looking for the derivative of a function is similar to differentiating the function.

Given the function f(x) = 6x+2

The derivative of the function

f'(x) = 6

The derivative of the function at x= 1 will still be equivalent to 6 since 6 is just a constant.

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Verify the identity: (1-sinx)/cosx = cosx/(1+sinx)

Lisa [10]

For the answer to the question above,
Let's work with the left-hand side
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After you've times the top and bottom by 1+sinx, you get:

cosx(1+sinx) / (1-sinx)(1+sinx)

The denominator is a difference of squares, so you get 1-sin^2 x

what you have now is

cosx(1+sinx) / 1-sin^2x

You know that 1-sin^2x is equal to cos^2x

so know you have

cosx(1+sinx) / cos^2x

get rid of the cosx on top by simplifying and the cos^2x so that you're left with

(1+sinx) / cos x

Therefore cosx / 1- sinx = 1 + sinx / cos x

4 0

3 years ago

The ratio of men to women working for a company is to 8 to 5 . If there are employees total 208 , how many women work for the co

Vikki [24]

Answer:

130

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5/8×208=130

8 0

2 years ago

Read 2 more answers

Solve for x.

Daniel [21]

Answer:

$x=-\frac{9}{4} \\ or \:\\x = -2\frac{1}{4}$

Step-by-step explanation:

$-2 (x + 1/4)+1=5\\\\-2\left(x+\frac{1}{4}\right)+1=5\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\-2\left(x+\frac{1}{4}\right)+1-1=5-1\\\\Simplify\\-2\left(x+\frac{1}{4}\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x+\frac{1}{4}\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x+\frac{1}{4}=-2\\\\\mathrm{Subtract\:}\frac{1}{4}\mathrm{\:from\:both\:sides}\\\\x+\frac{1}{4}-\frac{1}{4}=-2-\frac{1}{4}\\\\Simplify\\x=-\frac{9}{4}\\\\x = -2\frac{1}{4}$

4 0

3 years ago

4. What is the circumference of a circle whose area is 81π cm squared?

vichka [17]

Area = pi*r^2
Circumference = 2pi*r

Step 1: find the radius from area
81pi=pi*r^2
81=r^2
9=r

Step 2: plug in radius to the circumference equation

Circumference = 2pi*r

18pi is the answer, otherwise know as 56.52 as well.

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3 years ago

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yuradex [85]

6 in is the length cause yhu have to multiply

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