sin - if x # 0 Ex: Let f: [0,1] → R such that f (x) 1 if x = 0 f satisfy mean value property and f discontinuous function.

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…

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A: Given that: f(x)=x2-7,       0<x≤b6/x   ,        x>b

Q: Use a computer algebra system to analyze the function over the given interval.…

A: Consider the provided question, Analyzing the given function over the given interval using computer…

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Q: sin z Find the derivative of the function g(x) = V1+ 2t dt using the Fundamental Theorem of…

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Q: 3. Consider a function f(x) = sin() : R → R. x²+1 (a) Show that f is continuous on R.

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Q: sin i dt 48. Let F(x) = | Show that x3 F(x) = x - x5 x7 +... 3. 3! 5. 5! 7.7! Evaluate F(1) to three…

A: Given integral is: Fx=∫0xsin ttdt Fx=x-x33·3!+x55·5!-........... We have to find F(1).

Q: g(x) + a, (3 – b cos x, x > 0' Let f (x) be given by the function f(x) = where a and b are constants…

A: Given : fx = gx+a        … x≤03-bcosx     … x&gt;0 gx = 1-x2

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A: The given limit is, limx→01-cos(f(x))x2. Note that, the given limit is of the form 00. Apply L…

Q: x sin if x # 0 Show that the function f(x)= is differentiable at x = 3D0 and f '(0)= 0. if x = 0

A: A  function is  differentiable at  point c if L f'c=R f'cwhere L f'c=limx→c-fx-fcx-c   =left hand…

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A: Given f(x) = 1+sin2xx2

Q: 3. Give the definition of a continuous function (at a point ao) of one variable. Find (if possible)…

A: The function is said to be continuous at x0 if limx→x0f(x)=f(x0) where both limx→x0f(x) and f(x0)…

Q: Estimate `sin(-0.01)` using an appropriate linear approximation L(x) = f(a) + f'(a)(x – a).…

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Q: sin z Prove that lim Cosz - = 1 and lim = 0. Z→0 Z Z→0 Z Hint: use the definition of the derivative,…

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Q: -2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: The function f(x) =xsin). when x is not 0 and f(0) =0 is continuous at x-0.A O not continuous at…

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Q: sin(- ). if x+0 Q1: Determine whether f(x)= is of bounded variation on 0 , if x=0 [0,1].

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Q: ition of cont s continuous at the given point. a). f(x) = , a = 3 Use the 2z– -32

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider the function f(x) = x|x|. a.) On the interval (-∞o, 0), f"(x) = 0 b.) On the interval (0,…

A: topic - derivative of a function

Q: (c) A non-constant function f : [0, 1] →R such that f(x) > 0 for any r € [0, 1] but | f(x)dx = 0.…

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Q: onsider the function f(x) whose second derivative is f''(x) '(0) = 4, what is f(5)? 4x + 10 sin(x).…

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Q: 3. Find the constant "a" such that the function is continuous on the entire number line. 4 sinx x< 0…

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Q: Fihd f if f"(±) = sin(z), f(0) = -1, f'(0) = -1, f"(0) = -4. %3D f(z) =| D

A: Given: f'''(x)=sin(x),  f(0)=-1,  f'(0)=-1,  f"(0)=-4

Q: find a non zero value for the constant k that makes the function fx={tan k(x) /x ,x0}continuous at…

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Q: sin πx , x 2. 4 If the function f(x) is continuous at the point x= 0. then what is the sum of…

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Q: sin () if x + 0, COS X Let f : R → R be the function given by f(x) if x = 0. -1

A: The function  f:ℝ→ℝ is defined as follows: fx=sin1xcosx  if  x≠0-1                    if  x=0…

Q: sin(3t) i+ In(tan(6t)) -j+(t – 2) cos(3t) k , find lim F(t). t+0+ Let F(t) sin(6t) In(sin(3t))

A: solve the following

Q: 11 sin () Calculate the average of f(x) = over the interval [1,2]. (Use decimal notation. Give your…

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Q: sin(t) х Suppose F(x) = dt. Use the Fundamental of Theorem of Calculus to calculate dx :(F(x')). 6+t…

A: Given

Q: Test for homogeneity of the following and state the degree of homogeneity: 2. XZ f(x, y) = sin -3z

A: Given,   To Test f(x,y)=sinxzy-3zfor homogeneity and also degree of homogeneity

Q: X* sin if x + 0 Show that the function f(x)= is differentiable at x = 0 and f '(0) = 0. X if x = 0

A: Proceed as shown below...

Q: a tan(x) +b ,x0 so that f(x)={ cx +x+4b ,x=0, is continuous at b(2-x) x=0.

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Q: 1. Use the fundamental theorem of calculus part 1 to compute the derivative VI-t²dt. cos(z) dr

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

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Q: ( g(x) + a, xsO 13-b cos x, x>0 Let f(x) be given by the function f(x) = where a and b are constants…

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Q: Sx²-x²+1 1-sin x if x20 ) Let f(x) be defined as f(x)={* 0>x Is f(x) differentiable at x = 0? a) Is…

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Q: sin x At what points is the function y = continuous? 4x

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Q: sin(2(a? + y?)) 2(x2 + y²) f(x, y) sint as (x, y) → (0,0). Assume that polynomials, exponentials,…

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Q: sin 3x .cot 5x lim x→0 X cot 4x 2 t+ sin t lim t + co s t

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Q: C What is f" (x) of f(x) = x Arc sin(x) + √1 − x²? Arc sin(x) 2 √1-2² √1-7² ◄ Previous + Arc sin(x)

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Q: sin(1) Suppose F(x) = dt. Use the Fundamental of Theorem of Calculus to calculate dx (F(x). 9+1 (F<)…

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Q: 1 f(x) = sin - f' (æ) = Let 1 g(x) = sin x g'(x) =

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Q: tanx If f(x)= | V1+ x² - for all x€[0, 1/2], then f'(x) equals 1+ ex 0.

A: The differentiation of an integral can be obtained by using the second fundamental theorem of…

Q: Some type of phenomenon occurs at x=0 for the function f(x)=cos x-x^2 sinx, f(0) is a(n) A. maximum…

A: Given the function is f(x) = cos x - x2 sin x

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A: using first derivative test to determine function is increasing.

Q: 9 sin () Calculate the average of f(x) = over the interval [1, 2]. %3D (Use decimal notation. Give…

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Q: sinx +cos, x 0 Q4) Show that the function f(x)= is continuous at x 0 2, x 0 Q5) Determine the value…

A: See the attachment

Q: sin(t) Suppose F(x) = dt. Use the Fundamental of Theorem of Calculus to calculate F'(x). 3 +t 6.…

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