Let f(æ) = 9 sin(x). %3D a.) |f'(x)| < b.) By the Mean Value Theorem, f(a) – f(b)| < la – b| for all a and b.

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Q: Determine the values of a, b, and c so that the function (sin(a + 1)x + sin x x0 is continuous for…

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Q: find the absolute extrema of the function on the closed interval. g(x) = 2x + 5 cos x, [0, 2pie]

A: Here the given equation is g(x) = 2x + 5 cos x, [0, 2π] First we have to find the first derivative…

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: (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: Consider the functionsƒ(x) = sin x and g(x) =4∏2 x(∏ - x).Compute and compare the average values of…

A: Average value of f(x)=sinx on [0,π] is given by: Average value of f(x) is 2/π.

Q: If f(x) = –3x + sin(47x) for x E [0, 1], find the smallest value of c E (0, 1) which satisfies the…

A: The Mean Value theorem states that for a continuous and differentiable function f(x) on the interval…

Q: B-Test and proof the function So (x In x)² dx

A: ∫01(x logx)2dx=∫01x2 (log x)2dx use integral by parts, ∫udv=uv-∫vdu u=(logx)2…

Q: 36 If f is continuous and f(x) dx = 6, find xf(x²) dx.

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Q: It is known that the range of the function f(x)= a sinx+1 for xER is -2<f(x)≤4, then a = ?

A: Given fx=asin x+1,     ∀x∈ℝ range of fx is -2≤fx≤4

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Q: If f(x) is odd and ∫-1 to 5 f(x)dx=11 then, ∫1 to 5 f(x)dx=?

A: It is given that f(x) is odd and

Q: Let f be a function which is continuous, differentiable , and holds -1s f(x)<1 over the interval 0,…

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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: Find a value of c that will make the following function continuous at x = 0. sin² 4x x ≤ 0 x² f(x) =…

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Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

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: Find the mean value of sin 2x over the interval (0,x)

A: Solution is given below:

Q: Find f'a) for f(x)= =Sinx 1- Cos X %3D

A: We have to find the derivative of the given function.

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

A: The local extrema of a function can be obtained by equating the first derivative of the function to…

Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

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

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Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: 2n2 Using the mean-value theorems, show that in sin z w/6

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Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: 9. If f is continuous and f(x) dx = 14, find f(2x) dx.

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Q: Find f(x), where f'(x) = sin(x) + cos(x) + 1 and f(T) = 2.

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Q: Find the constants "a" and "b" so that the following function (sin 2x, if 0<xs. sin 2x, if 0 < x < f…

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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: Consider y=xsin(pi)x over [0,2] Verify the mean value that applies and find all values c satisfying…

A: Find values of c satiating the Mean Value Theorem

Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(T) = 2.

A: We have to find

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Let f (x) = 3 sin(2x) – 3 cos(3x). Find the values for the constants in the derivatives f' (x), f "…

A: We have to find the constant

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

A: A detailed solution is given below

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: Q3) a) 42? Use Mean value theorem to show that for all a E (0, , 4 tan z 2

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Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: Let f (x) = sin(x) – x. %3D Then f' (0) = 0. and f " (0) = |0 However, f (0) is not a relative…

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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: Evaluate sin (x) e-x dx by use Simpson's rule. h=0.5

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Q: Evaluate f(x) dx, where 8x', ={ 7 sin(x), 0<x< a. -T < x < 0 f(x) :

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Q: a. Find the root mean square value of tanh x, for 0 < x< 2.

A: we know the formula of root mean square, rms = [ (1/b-a) (integration of |f(x)|2 from a to b) ](1/2)…

Q: d Prove, through the limit process, that (cos x) = - sin x. dx

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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: sin(bx) x0. Find a value of b such that f is continuous, or explain why no such value exists.

A: Given, f(x)=sin(bx)xx&lt;0exp(x+5)x≥0