Let L be the tangent line to y=tan(2x) at (pi/2,0). What is the y-intercept of L? (a) 0 (b) pi/2 (c) −pi (d) 1 (e) 2

Kelton Molina

Kelton Molina

Answered question

2022-09-24

Let L be the tangent line to y = tan ( 2 x ) at ( π 2 , 0 ). What is the y-intercept of L?
(a) 0
(b) π 2
(c) π
(d) 1
(e) 2

Answer & Explanation

Absexabbelpjl

Absexabbelpjl

Beginner2022-09-25Added 8 answers

The equation of the tangent line at the point ( a , f ( a ) ) is
L ( x ) = f ( a ) ( x a ) + f ( a )
In this case, f ( x ) = tan ( 2 x ) and a = π / 2. Hence
L ( x ) = 2 sec 2 ( 2 π 2 ) ( x π 2 ) + tan ( 2 π 2 )
i.e. L ( x ) = 2 ( x π 2 ) = 2 x π. Therefore, the 𝑦-intercept of L is π.
mundocromadomg

mundocromadomg

Beginner2022-09-26Added 3 answers

The tangent to the curve y = f ( x ) at the point ( t , f ( t ) ) is the line
y f ( t ) = f ( t ) ( x t )
The y-intercept of this line is the point where x = 0 and hence
y = f ( t ) t f ( t )
Can you solve it now?

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?