Show that (i) tan x < x, 0

Q: dx - = In[F(x)]+C•What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) -1 + - -1

A: Solved below

Q: (a) f(x) = sin(x) X at x = 0.

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

Q: 4. How many fixed points does the function T(x) = tan(x) have? %3D

A: for fixed point f(x) = x x = tan(x)

Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

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Q: defines eX-e-x O a. tanh x Оb.csch x O c. sinh x

A: 2ex-e-x=?

Q: 1 Let f(x) = (5 sin x + 8 cos a)tan f'(x) =

A: NOTE: Refresh your page if you can't see any equations. . take derivative use the product rule for…

Q: Find the absolute extrema of the function on the closed interval.                    f(x) = sin 2x,…

A: Approach: Without wasting any time, take the derivative of the original function. Find critical…

Q: what values of x is f(x) = 2 tan(x + π/6) discontinuous?

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Q: 1 Let f(x) (5 sin x + 4 cos x æ)tan- f'(x) =

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Q: prove that f(x) = sin*x + cos*x is a periodic function with periods

A: We use the Given Equations Prove that f(x) is a periodic function with period pie/2.

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

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Q: What is special about the functions f(x) = sin x - 1 x + 1' x 2 0, and g(x) = 2 tan Vĩ? -1 Explain.

A: Given that functions are f(x)=sin-1x-1x+1, x≥0 and g(x)=2tan-1(x). The graph of the function…

Q: Determine values of a and b that make the given function continuous: if x 3

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Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: 1. If tan-1 x x 1’ f(x) = Then S(x) dx =?

A: This question is related to definite integration, We will solve it using given information.

Q: List the x values of the discontinuities of the function below: y = In (tan²(x)) over the interval…

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Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: y=x-2cosx Differentiate the function. dydx=ddx(x-2cosx)=1+2sinx

Q: Estimate the error if P3(x) = x - (x3&gt;6) is used to estimate the value of sin x at x = 0.1.

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Q: If f(x) = COS x 3 tan x, then find: | f'(x) = f'(1) =

A: Given  f(x)=cos x-3tan x

Q: Is the function f(x)=sin(3x)+cos(tan x) even, odd, or neither? Why?

A: Recall: A function f(x) is even if  f(x) =f(-x). A function f(x) is odd if f(x)=-f(-x)

Q: 4. How many fixed points does the function T(x) tan(x) have? %3D

A: As per our guidelines, we suppose to answer only one question. Here question 4) is answared.

Q: (B) The evaluation of f- -dx is (x*+3x2 +1)[tan-( In|tan"+5| + e -In tan-( +c (i) (ii) (iii) None of…

A: No antiderivative could be found within the given time limit, or all supported integration methods…

Q: Find the limit of tan(4x)/sin(6x) as x approaches zero.

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Q: Find the absolute extrema on the interval [0,2π] for f (x)=x/2+cos x.

A: Absolute extrema

Q: Let f(x) = (7 sin x + 2 cos x)tan-lx f'(x) = %3D

A: topic - derivatives

Q: 2x + a + 1 if – 1< x < 0 Let f (x) = { x*sin (if 0<xs1 x*sin if 0 ) <x< 1

A: Given that f(x)=2x+a+1-1≤x≤0x4sin1x0&lt;x≤1 It is true that the function is continuous at [-1,0) and…

Q: 2. Find all values of 0 in the interval [0°, 360°) that have the given function value tan 0 = -V3.

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Q: Find the absolute extrema of the function on the closed interval.

A: The given function is y=tanπx8    on  0, 2. Compute the critical points as follows.…

Q: The derivative of In (cos x) is A -tan x B None of the given choices tan x D sec x -sec x

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Q: If f(x)=tan x, then show that f(x+y)-f(x) = sec^2x tany/ 1-tanxtany

A: The detailed solution is given below Thank you

Q: If f(x) = cos cos x – 7 tan x, then | f'(x) = f'(3)

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Q: Let f(x) (3 sin a + 2 cos x)tanx f' (x) =

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Q: Find f'(x) for f(x) = sin?x · tan (x² – 3x + 1)5).

A: We will find the derivative.

Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(7) = 2.

A: Given: f'(x)=sin(x)+cos(x)+1 and f(π)=2

Q: 1. What is f tan x dx?

A: we have to determine what is ∫tanx dx let the integral be I. therefore, I=∫tanx dx as we know that…

Q: Find the extreme values for the function f(x) = x + sin x on the interval [0, 27).

A: This function is unbounded below and unbounded above, Therefore the function has no global extreme…

Q: Use the Intermediate Value Theorem to show that f(x) = 2+ sin r 3 tan x has a | (0. ). solution in…

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Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: The function f(x) sin x + cos x is an even function. True False

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Q: dx = In[F(x)]+C.What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1)

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Q: 1 Let f(x) = (8 sin x + 9 cos x)tan f'(x) = %3D

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Q: Find the indefinite integral. tan“ X dx sec x

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Q: calculate the value : f'(x) 3. a) f(x)=4xe**+ln(sin/x)+2cos(x³ +2x+1)

A: f(x) = 4xex3 + lnsinx + 2cosx3+2x+1f'(x) = ?

Q: Find the relative extrema of f(x) = 1/2x − sin x in the interval (0, 2pie ).

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: f(x) = /tan-1 (cos x) + In(sec x)

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Q: Find the derivative of

A: Given,

Q: f(x) = x in the %3D sin 2x + ...

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Q: S [tan® x sec6 x + cos“ x sin“ x + sin* x] dx

A: Given that: (tan8xsec6x + cos6xsin4x+sin4x) we solve this integration by using general formulas of…

Q: Find the function f(x) if f'(x) = 2 cos x + 3 sin x and f(0) = 4

A: We have