Determine f such that (1, sin 1) is on the graph of f and e2z + 5e² + sin x ifæ <0 6ez f'(x) = . ifæ = 0 Va (x2 +1) + cos æ ifæ >0

Q: 10. Approximate a value of z e [0,1] so that the length of the graph of f(x) tan(vx2 + 1) on [0,z]…

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Q: 103. GU Plot the graph of f(x) sin mx sin nx on [0, 7] for the pairs (m, n) = (2, 4), (3, 5) and in…

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Q: Let f(x) = 3 cos 2x + sin² x. a) Show that f'(x) = -5 sin 2x. 3π b) In the interval 프 <x< 4 one…

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Q: 8 sin x Find an antiderivative F(x) of the function f(x) such that F (0) = 1- 3 + cos r

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Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

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Q: 1) Match each function with its gray-Cos Cos x y = Sin x y=-Sin x y =-Cos x Slide correct function…

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Q: So, 0, -T < x < 0 f (x) = sin x, 0 < x < T

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Q: If f( x ) = sin (x) – e“ , what is f'(x) ? O f'(x)=- cos(x)-e² — сos(2) —е* O f'(x)=sin (x) –e² O f…

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Q: a. Let ƒ(x) be a function satisfying 0 ƒ(x) 0 … x2 for -1 … x … 1.Show that ƒ is differentiable at x…

A: The differentiability of the function can be determined with the help of the left-hand derivative…

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: Suppose f and f' are differentiable functions of r. Given f' () = 0, f" () -1, and g(x) = log…

A: Differentiate two times at given value

Q: * 3x ], the x-coordinates of the points on the graph of the function f(x) = 1 + cos x where the…

A: For horizontal  tangent dy/dx=0

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: plot the function and use the graph to estimate the value of the limit.

A: Using the graphing utility, we get following graph of function

Q: Given f (x) = |x| for x E [–n, 1] Show that 4 cos(2n – 1)x |x| = 2 E - - - (2п — 1)2 n=1

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Q: #2. Verify Clairaut's Theorem for the given function f (s, t)= In (st)-s* sin (6t) +st.

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Q: 2. Let f(x)=3 cos 2x + sin²x. a) b) Show that f'(x) = -5 sin 2x. In the interval <x<³ Find the value…

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Q: For the function f (x) = cos² x – 2 sin x, find the interval(s) on which f (x) is…

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Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: Find the open intervals on which the function is increasing or decreasing.       y = x − 2 cos x, 0…

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Q: For f(x)=-cos(x)-1, choose all values of c in the interval (pi/2,5pi/2) guaranteed by Rolle's…

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Q: 2. Let f(x) = 3 cos 2x + sinx. a) b) Show that f'(x) = -5 sin 2x. π 3π In the interval <x< one…

A: We need to find derivative and normal.

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: - cos(x) - 1, choose all values of c in the interval (, 5 For f(x) guaranteed to exist by Rolle's…

A: For fx=-cosx-1, choose all the values of c in the interval π2,5π2guaranteed to exist by Rolls's…

Q: The derivative of f(x) = tan- is: Select one: O a. O b. O C. O d. 1 x² cos² 1 -1 x² cos² 1 xcos² 1 F…

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Q: The function f(x) 22 e sin x+2x 5 cos x + has a removable discontinuity at a = 0. To remove the…

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Q: Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)? What is…

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Q: Find the points of inflection,smaller x-value,and larger x -value  of the graph of the function. (If…

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Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: 1. Determine the absolute extrema of f(x) = (sin x – 1) cos x on 2' 2 if they exist, and identify…

A: Given:-f(x)=sinx-1cosx,        x∈-π2, π2f'(x)=sinx-1ddxcosx+cosxddxsinx-1…

Q: 4 cos (2x e function f is defined by f (x) values of x on the interval (0, 3 such that the line…

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Q: e sin a – x lim 10 10 cos x- 10 O - 0.2000 | O 0.1000 O - 0.1000 O 0.2000

A: Use L hospital's rule as it of indefinite form. So differentiate the numerator and denominator both…

Q: Find f if f^ prime prime (x)=sin x+cos x,f^ prime (0)=4 , and f(0) = 3

A: The differential equation is given by f''x = sinx+cosx                ........1 The initial…

Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

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Q: 17. If g(x) = ln(cos x), what is g'()?

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Q: 1. Determine the absolute extrema of f(z) = (sin a – 1) cos z on -. 2 if they exist, and identify…

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Q: a) If n is a positive integer, prove as given in image (b) Find a formula for the derivative of y…

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Q: Q5) Find f((s) if you know that g(x) = cos(x² – 1). S(x) = 3tan(x*) at vr?

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

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

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Q: Determine if g is differentiable at a = 0 if 2 cos-1 if – 1 0. x + cos x

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Q: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) >= 0 for x element…

A: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) &gt;= 0 for x element…

Q: 1. Find the value/s of b such that the function ƒ is continuous everywhere. f(x) = {6x – sin bx 0 <x

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Q: Let f(x) = 3 sin'x - 7 cos(2x), 0 <xS T. Find the interval(s) on which f is increasing. (A) (0, 7)…

A: Recall that, f is increasing on (a,b) if f'(x)&gt;0 in (a,b).

Q: Let f(x) = 3 cos 2x + sin² x. a) Show that f'(x) = -5 sin 2r. b) In the interval <x<³7, one normal…

A: Use equation of normal

Q: Find the first and second derivatives of each function. (a) f(0) = 3 cos(e) 5 (b) f(x) = x³sin(x) +…

A: a) f(θ)=cos θ3+5θb) f(x)=x3sin(x)+3cos(x)c) f(x)=e-3x+ln x-7x Note: Multiple parts are given, we are…

Q: A pdf is given by 2 cos (x 3 ").0<x< f(x) = 3 Show that this is a valid pdf and then find P(X<1).

A: Topic:- probability

Q: If g(x) f'(x) and if g(x) (cos x - x sin x)e*cosx, then f g(x) tan(f(x))dx is x cosx In(e*cosx) +€…

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