If g(x)=x/1+2x, how do you find g'(a) and use it to find an equation of the tangent line to the curve at the point (1, 1/3).

equation of tangent at (1,1/3) is:

Step-by-step explanation:

this differentiation can be easily done using the quotient rule:

here,

u = x, and v = 1+2x.

u' = 1, and v' = 2

The derivative of u and v are written as u' and v'.

this is the derivative of g(x) and it is denoted by g'(x)

g'(a) means to simply replace all the x's with a in the above equation

to find the equation of the tangent to this curve at (1,1/3)

we need to know the slope of the tangent at that very point. This can be found using g'(x). since g'(x) only takes x as the input. we'll only use the x-coordinate of the point (1,1/3)

the slope of the tangent to the curve at the point (1,1/3) is 1/9

to find the equation of the line we'll use:

here m is the slope, and (x1,y1) = (1,1/3)

simplify:

this is the equation of the tangent to the curve g(x) at the point (1,1/3)

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

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step-by-step explanation:

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