1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = %3D 1+cos 2 x

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps
that: cos? x =
1+cos 2 x
2) Find in steps: lim x2 sin -
X-0
-x + 1, x 2 0
3) Let f (x) =
sin x
x² +
-2
(a) Find left-hand and right-hand limits as "x" approaches "zero".
(b) Does lim f (x) exist? Why?
4) Find an equation of the line through the point (3, 2) that is parallel to the line
2x + y +5 = 0.
5) Find the vertex, x-intercepts, and y-intercept, and graph the equation
y = -x2 +x + 4.
6) What is the domain and associated range of y = v8 + x3
V
Transcribed Image Text:1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = 1+cos 2 x 2) Find in steps: lim x2 sin - X-0 -x + 1, x 2 0 3) Let f (x) = sin x x² + -2 (a) Find left-hand and right-hand limits as "x" approaches "zero". (b) Does lim f (x) exist? Why? 4) Find an equation of the line through the point (3, 2) that is parallel to the line 2x + y +5 = 0. 5) Find the vertex, x-intercepts, and y-intercept, and graph the equation y = -x2 +x + 4. 6) What is the domain and associated range of y = v8 + x3 V
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