Difference between revisions of "009A Sample Final 3, Problem 10"

Revision as of 19:36, 17 February 2017

Let $y=\tan(x).$

a) Find the differential

dy

of

y=\tan(x)

at

x={\frac {\pi }{4}}.

b) Use differentials to find an approximate value for

\tan(0.885).

Hint:

{\frac {\pi }{4}}\approx 0.785.

Solution:

(a)

Step 2:

(b)

Step 1:

Step 2:

(c)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam">Let <math>y=\tan(x).</math>
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::<span class="exam">a) Find the differential <math>dy</math> of <math>y=\tan (x)</math> at <math>x=\frac{\pi}{4}.</math>
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+::<span class="exam">b) Use differentials to find an approximate value for <math>\tan(0.885).</math> Hint: <math>\frac{\pi}{4}\approx 0.785.</math>
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"