Meet students taking the same courses as you are!Join a Numerade study group on Discord

The point $P(0.5, 0)$ lies on the curve $y = \cos \pi x$.(a) If $Q$ is the point $(x, \cos \pi x)$, use your calculator to find the slope of the secant line $PQ$ (correct to six decimal places) for the following values of $x$: (i) $0$ (ii) $0.4$ (iii) $0.49$ (iv) $0.499$ (v) $1$ (vi) $0.6$ (vii) $0. 51$ (viii) $0.501$(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at $P(0.5, 0)$.(c) Using the slope from part (b), find an equation of the tangent line to the curve at $P(0.5, 0)$.(d) Sketch the curve, two of the secant lines, and the tangent line.

A.SEE TABLEB.$$-\pi$$C.$$\rightarrow y=-\pi x+\frac{\pi}{2}$$D.$=(1,-1.000000)$

Limits

Derivatives

Discussion

You must be signed in to discuss.
NH

September 22, 2020

what is decimal places?

ST

Samantha T.

September 22, 2020

Hey Nadia, A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol also affec

ST

Samantha T.

September 22, 2020

LP

Lindsey P.

September 22, 2020

I'm confused by the term cosign?

AG

Alex G.

September 22, 2020

I know this one! The length of the adjacent side divided by the length of the hypotenuse. The abbreviation is cos. cos(?) = adjacent / hypotenuse. Well Done! Another.

HC

Howie C.

September 22, 2020

Anyone else confused by the slope, can someone explain?

CR

Cam R.

September 22, 2020

I see how that could be confusing. In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Lectures

Join Bootcamp

Video Transcript

Topics

Limits

Derivatives

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Lectures

Join Bootcamp