Answered: 4) dependent Show that the following… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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4)
dependent
Show that the following set of functions is Linearly independent or linearly
fi(x) = sin²x, f₂(x) = 3, fs(x) = cos²x

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4. Find two possible non-linear functions and goh sinx- x² such that
Solve q. Find the derivative of f.
{sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I = (-∞,∞) Determine if the set sinx,
2. a. f(x) = (x+2)/(x +4). Use the Mean Value Theorem on the interval [0, 4] to find all values of x in the interval (0, 4) such that the value of the first derivative of f at those points is (f(b) – f(a))/(b – a). b. For the interval [-5, 0], fb) - fa))(b — а)-GG0) — f-5)(0 — (-5)) = (½ – 3)/(0 + 5) = -½ but, since the first derivative of f(x) is always positive, nowhere on that interval does the first derivative of f(x) = -½. Thus the Mean Value Theorem does not hold for f(x) on this interval. Why?
1. Find the derivative function for the following using the power rule: a) f(x) = x¹2 b) y = 8x³ - 2x + 12 c) h(k)= d) f(a)= 2-5k³ k2 (2a-1)² 2a + 5a
6) When some variable z is a function of time (t), the derivative of z with respect to t is denoted using the "dot" notation: * = r(t). If a(t) and b(t) are positive-valued differentiable functions of time (t), and if A, a, and 3 are constants, find expressions for i/x where (a) r(t) = (a(t))² b(t) (b) x(t) = A (a(t))a (b(t)) ³ a+B (c) z(t) =A((a(t))° + (B(t))) a
2. Differentiate the following function f(x). If it is not differentiable, state your reasons. Otherwise compute the f' (x). (You can use those techniques in section 3.3 for this problem) = cos et cos z f(x) = 23

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