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5. Consider the function f(x) = tan x, π/2

5. Consider the function f(x) = tan x, π/2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I am having trouble with the graphing on each of these.

I have taken a picture of my answer so far, can you help me see if I am on the right track?

5. Consider the function f(x) = tan x, -π/2<x<π/2. (a) Use the quotient rule to find an equation for the tangent line to the curve y = f (x) at the point (0, 0). Sketch a graph of the function f (x), including the tangent line in the graph. = (b) Use the substitution rule to find the area under the curve y = f (x) from x your answer. Sketch another graph of the function f (x), now shading the given region. 0 to x = π/4. Simplify
Transcribed Image Text:5. Consider the function f(x) = tan x, -π/2<x<π/2. (a) Use the quotient rule to find an equation for the tangent line to the curve y = f (x) at the point (0, 0). Sketch a graph of the function f (x), including the tangent line in the graph. = (b) Use the substitution rule to find the area under the curve y = f (x) from x your answer. Sketch another graph of the function f (x), now shading the given region. 0 to x = π/4. Simplify
0 I4 I 3 I 2, II I. II 4, 15, 5) f(x) = tan (x) => f'(x) = m d => m= & tan (x) = — Sin(x) dx Cos(x) => m= cos(x) ((cs (x)) - Sin(x) (- Sing 2 Ccs² x =) m = cos² (x) + Sin ² (x) Zm= 2 cos² (x) => m = Sec²(x) At paint (0,0) ! m = Sec² (0) = 1 2 cos x x = x Equation of (x-0) = m (x-0) y = 1(x) the tangent! اسکار Y (0,0)
Transcribed Image Text:0 I4 I 3 I 2, II I. II 4, 15, 5) f(x) = tan (x) => f'(x) = m d => m= & tan (x) = — Sin(x) dx Cos(x) => m= cos(x) ((cs (x)) - Sin(x) (- Sing 2 Ccs² x =) m = cos² (x) + Sin ² (x) Zm= 2 cos² (x) => m = Sec²(x) At paint (0,0) ! m = Sec² (0) = 1 2 cos x x = x Equation of (x-0) = m (x-0) y = 1(x) the tangent! اسکار Y (0,0)
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