What is the equation of the line tangent to f(x)=sin⁡πx at x=1?

For f(x)=sin⁡(πx), we get f(1)=sin⁡π=0andf′(x)=cos⁡(πx)[ddx(πx)]=cos⁡(πx)[ddx(πx−1)]=cos⁡(πx)[−πx−2]=−πx2cos⁡(πx)So, f′(1)=−πcos⁡π=πThe line through (1,0) with slope m=π isy=πx−π

"What is the equation of the line tangent..." was answered by our experts

High School
Calculus and Analysis
Calculus 1
Derivatives

Bryant Miranda

Answered question

2022-02-12

What is the equation of the line tangent to

f (x) = \frac{\sin π}{x}

at x=1?

Answer & Explanation

ljmolerovae

Beginner2022-02-13Added 15 answers

\sin π = 0

, so, for all

x \neq 0

, we have f(x)=0.
Therefore, f'(1)=0. (By definition or by properties/rules for differentiation.)
At the point where x=1, we get y=f(1)=0,
and the equation of the line with slope m=0 through (1,0) is y=0

golfachukc8

Beginner2022-02-14Added 13 answers

For

f (x) = \sin (\frac{π}{x})

, we get

f (1) = \sin π = 0

and

f^{'} (x) = \cos (\frac{π}{x}) [\frac{d}{d x} (\frac{π}{x})] = \cos (\frac{π}{x}) [\frac{d}{d x} (π x^{- 1})]

= \cos (\frac{π}{x}) [- π x^{- 2}] = - \frac{π}{x^{2}} \cos (\frac{π}{x})

So,

f^{'} (1) = - π \cos π = π

The line through (1,0) with slope

m = π

y = π x - π

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f (x, y) = x^{3} - 6 x y + 8 y^{3}$
$\frac{1}{\sec (x)}$ in derivative?
What is the derivative of $\ln (x + 1)$ ?
What is the limit of $e^{- x}$ as $x \to \infty$ ?
What is the derivative of $f (x) = 5^{\ln x}$ ?
What is the derivative of $e^{- 2 x}$ ?
How to find $lim \frac{e^{t} - 1}{t}$ as $t \to 0$ using l'Hospital's Rule?
What is the integral of $\sqrt{9 - x^{2}}$ ?
What is the derivative of $f (x) = \ln [x^{9} {(x + 3)}^{6} {(x^{2} + 7)}^{5}]$ ?
What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?
How to find the derivative of $y = e^{5 x}$ ?
How to evaluate the limit $\frac{\sin (5 x)}{x}$ as x approaches 0?
How to find derivatives of parametric functions?
What is the antiderivative of $- 5 e^{x - 1}$ ?
How to evaluate: indefinite integral $\frac{1 + x}{1 + x^{2}} d x$ ?

Didn't find what you were looking for?