A. Using Mean Value Theorem prove that sin r– sin y| <|r-y for all I,y € R.

Q: 1/x tan TC + x f(x)= .For what value of k, f (x) is k, continuous at x 0?

A: Introduction :We have given a function f(x) we have asked to calculate the value of k , if f(x) is…

Q: sin(t) ppose F(2) = ) dt. Use the Fundamental of Theorem of Calculus to calculate F' (1). 9+t (z) =

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Q: [sin (zx), 0<x<1 lax+b, 1<x<4 17. Let f (x)= { f(x) is Find the values of a and b such that…

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Q: discuss the continuity of the function. a) f(x,y,z)=z/(x^2+y^2-4) b)f(x,y,z)=xy sin z

A: (a) consider the provided question,   fx,y,z=zx2+y2-4  The given function is continuous except at…

Q: The line y =x+1 is the tangent line to the graph of the function O (A) f(x) = x³+1 at the point (1,…

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Q: Evaluate F- dr where F = (3z, y, 4x), and C is given by 7 (t) = (sin(t), cos(t), t), 0 <t<T

A: We have F→=3z,y,4x and r→t=sint,cost,t, 0≤t≤π. Then we have to evaluate ∫CF→·dr→

Q: Find a and b such that f is differentiable everywhere.

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Q: For what value of the constant c is the function f continuous on the interval (-o, 0o). - Scr+ 3z, I…

A: Explanation of the answer is as follows

Q: If f(x) = xtan(), then f'(x) = %3D (A) (In(x) + tan(e)) xtan(2) (B) sec²(x) In(x) ætan(z) (C)…

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Q: 1. Find the absolute extrema of the function f(r) = e sin r-sin r+cos z in the interval [0, "]. %3D

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Q: Prove the Bolzano's Theorem for the case f(a) > 0 and f (b) < 0. .

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Q: Find f'(x) and f'(c). Function f'(x)= f'(c) = f(x) sin x x Value of c π 3

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Q: (a) Use the Product Rule twice to prove that if f , g , and hare differentiable, then (fgh)'   =f'gh…

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Q: 1/x TC tan + x f(x)= For what value of k, f (x) is k, continuous at x = 0? %3D

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Q: x+ y Let f(x) = and ɛ = 0.02. Use definition of limits 2+cos x to find 8 > 0, such that for all…

A: answer

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

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Q: 16. Let f(x) be a differentiable function defined on [0, 2] such that f (x) = f (2 - x) for all x e…

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Q: Given: f(x, y) = ln[1 + x siny] Find: 8² f(x,y) 8x² 2 sin y (1+xsin y)² ○ _ __ sin² y (1+zsin y)²…

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Q: a) f(x) = 1+ Sinx for all x e R

A: According to the question, we need to plot the graph of the function: f(x) = 1+sin x The graph of…

Q: Suppose that f(x) is a differentiable function, and let g(x)= f(e2x ·cos x). What is the value of…

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Q: (a) Integrate to find F as a function of x. (b) Demonstrate the second fundamental theorem of…

A: (a)  Given: F(x) =∫axsec t tan t dtFormula: ∫sec x tan x dx =…

Q: Cz sin r 5. If f : R → R is continuous, find F"(x) for F(x) = f(t) dt. %3D

A: F'(x) of the given function

Q: gercise:1- prove that (A – V)f (x) =AVf (x). 4 Evaluate sin(x + E h)

A: Note:"Since you have posted multiple question.As per our guidelines we are supposed to solve only…

Q: Study the measurability of the functions: (sinx,x e [0,1] – Q. | i-f (x) = } x3+6 x € [0,1] n Q…

A: Given: fx=sinx,x∈0,1-ℚx3+6x2+2,x∈0,1∩ℚ fx=sinx,x∈0,1-Px3+6x2+2,x∈P and P is not measurable subset…

Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: a) Find f'(x) for f(x) = sin?x · tan³((x² – 3x + 1)5). %3D (tan*/x) (sec²x) dx h) Evaluate

A: We have to find the derivative of f(x).

Q: Find a and b such that f is differentiable everywhere. f (2) = { 3 cos (x) if r 0 a = b =

A: Given: f(x) = 3 cos (x)               if x &lt; 0ax + b                 if x ≥ 0 To find: Values of…

Q: QI// Let f(x)= (1+sin?x) x2 then Limit of f(x) as x approached to %3D zero equal to:

A: Apply the limit to the function. limx→0f(x)=limx→0 1+sin2xx2=1+sin2002=10=Undefined Since the value…

Q: find fsub(x), fsub(y), and fsub(z): f(x,y,z)=e^(yz+sinx)        (All above e)

A: We have to find derivative

Q: 1. Consider the function Sa(1 – x) sin r€ (0, 1), πε (0, 1) , - f (x) = %3D (0, x € {0, 1}. (a)…

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Q: discuss the continuity of the function f. S(x, y, z) = Vxy tan z S(x, y) = /25 – x² – j

A: To find - Discuss the continuity of the function f. fx, y, z = xy tanz fx, y = 25 - x2 - y2

Q: Let f(x) = sin(rx). Suppose that h and k are two functions such that H (x) = cos(xx), k'(x) = f(x+…

A: Given that fx = sinπx . Also given that h and k are two functions such that h'x = cosπx , k'x = fx+1…

Q: az Let F(x, y, z) = z* +x+ y sin x + x In z = 0, where z = f(x,y), then at (0,0,1) and az are ду…

A: see 2nd and 3rd step.

Q: Let f(2) = (z - n) sin z. Find an che point a. integer n such that f is n-to-one near

A: Given, fz=z-πsinz Differentiating the given function. fz=z-πsinzf'z=z-πcosz+sinzf''z=-z-πsinz+2cosz

Q: a sin (), if (x, y) # (0, 0) 2. Determine if a function f: R? → R defined by (x, y) = 0, if (r, y) =…

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Q: Q1:Discussion a continuity of the function f(x, y) at the point (0,0), where rey sinx (x, y) = (0,0)…

A: Given that fx, y = ey sin xx , x, y ≠ 0, 01               , x, y = 0, 0 . We have to discuss the…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) +…

A: Consider the given function. Differentiate the above function with respect to x. Equate the above…

Q: Find all values of a for which f(x) is continuous where ´sin(x) I 0

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Q: •x sin t Let F(x) = | dt. Determine the largest interval containing 0 on which F(x) is non-negative.…

A: Step:-1 Given that Fx =∫0x sinttdt Now, to find the largest interval,  we'll use the graphical…

Q: Find the linearization at x = a. f(x) = sin° (x), a = %3D (Use symbolic notation and fractions where…

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Q: Using the Fundamental Theorem of calculus (o() e'dt)' is Jsin(x) 1. -sin(x)ecos(x) – cos(x)e*in(z)…

A: Ans. Is option 1.

Q: (a) Show that the function sin r is continuous in R. (b) Let I sin , r+0 g(z) = < 0, I = 0 Show that…

A: a) A function is said to be continuous at x=c if left hand limit and right hand limit of the…

Q: Discuss the continuity of the function. f(x, y, z) = xy sin z

A: Given- fx,y,z=xysinz To Discuss- The continuity of the above function. Concept Used- A function is…

Q: 2? sin ? a +0 x = 0 Let f(x) = (c) Show that f'is not continuous at x = 0.

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Q: F(x)= in for -くX (X) =<osXfor os:X いゴ, and h(x) = tan x for <x<I. Find each of the following…

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Q: 8b. Apply the Fundamental Theorem of Calculus II to find | (sin(x) + cos(x)) dx The Fundamental…

A: Here,  f(x)=sin x+cos x Now, F'=fF=∫f(x) dx because F is an antiderivative of f.

Q: Homework: 1. If y=tan x, prove that y`= 2(y +1)(3y² +1).

A: As per the guidelines I solve your first question. For more solutions please resubmit the question.…

Q: Q. Given f(x) = { 2+ x cos x if x >0 if x < 0 ,then 2 – x sin x | a. f is a continuous but not…

A: As Many, questions are given I will solve only one: We are given, the following: f(x)=2+x cos x,…

Q: 3. Proof that f (x) = x sin is continuos but is not differentiable at 0

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Q: 12. Let F(x, y) = esinx+cosy(cos x ,– sin y) and C = {(x, y): x² + y² 0. Show that F- dR = 0 Hint:…

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.