(a) Show the following identity: cos e 1+ sin e 2 sec 0 + 1+sin 0 cos e

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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ISBN:9781337111348
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Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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(a)
Show the following identity:
cos e
1+sin 0
= 2 sec 0
1+sin 0
cos e
x+1
using the limit definition of
2 -x
(b)
Compute the derivative of the function f(x)
derivative. Determine the domain of the function and its derivative.
(c)
Determine the derivatives of the following functions.
(i)
f(x) = 4x/x+ Vx
(ii)
f(x) = cos (ev
/tan 3x
1+csc x²
(ii)
f(x)
1- cot x2
(d)
The curve with equation 2 (x² + y²)² = 25 (x² – y²) is called the Lemniscate.
dy
by using implicit differentiation.
dx
(1)
Examine
(ii)
Determine an equation for the tangent line to the Lemniscate at the
point (3.1).
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Transcribed Image Text:< Edit (a) Show the following identity: cos e 1+sin 0 = 2 sec 0 1+sin 0 cos e x+1 using the limit definition of 2 -x (b) Compute the derivative of the function f(x) derivative. Determine the domain of the function and its derivative. (c) Determine the derivatives of the following functions. (i) f(x) = 4x/x+ Vx (ii) f(x) = cos (ev /tan 3x 1+csc x² (ii) f(x) 1- cot x2 (d) The curve with equation 2 (x² + y²)² = 25 (x² – y²) is called the Lemniscate. dy by using implicit differentiation. dx (1) Examine (ii) Determine an equation for the tangent line to the Lemniscate at the point (3.1). Rotate Crop Filter Splash Blur Adjust
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