The average value of a function f (r) over the interval [a, b] is given by farg Determine the average value of R(2) = sin (2:) el-cos(2:) on [-T, 7) .

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: 5. Find the third derivative of the function : 3 (ans. : - 8y y=Vx

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

Q: Find f. f"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4

A: Given functionf"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4we have to find , f(θ)

Q: find the average vaim of the function fcx) = x² = 5x + 6 cosx on th Interval [-1, [-1,3].

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Q: Find of the fo lloming function the derivative Tin C A y'= (Sinsc) oc Sin 6-1 Sinac +Inx cos scl +…

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Q: Find the derivative of y with respect to x for y= ( cos 7x) ot /X Choose the correct derivative of y…

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Q: 3 (a) Differentiate the left-side functions with respect to the right-side ones I+/(1+x³), i) tan…

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Q: Define f = sin(px^3)+cos(qx)^2 as a function of x (with p and q constant) and differentiate with…

A: see 2nd step.

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: Find f'(z) if f(z) = 8 cos(z) + 9 sin(z). Answer

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Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

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Q: Differentiate y = (ln r)tan 2x

A: We have to differentiate; y=lnxtan(2x)  taking natural logarithm both of sides;…

Q: x2 – 4 lim h→2 Vx – V2 /9 + h – 9 - lim h→0 h

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Q: Find points of horizontal and vertical tangent lines r = 1- cos(0) %3|

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Q: Find the domain and range of f(x,y) = cos-'(x – y)

A: This question is related to inverse trigonometry.

Q: tan(2x)=1 interval [0,2pi}

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Q: Find f. f"(x) = sin(x) + cos(x)   ,   f(0) = 3,  f'(0) = 4

A: Given:  f''(x) = sin(x) + cos(x)                                                (1)   Formulae used:…

Q: Let F be the function given by F (x) = S" (sec² (5t) – 1) dt. Which of the following is an…

A: We have given that   F(x) = ∫2x(sec2(5t)-1)dt        ...(1). And we have to find F'(x). To find the…

Q: Find the linearization at x=a and then use it to approximate f(b) 1.) f(x)=x4, a=1, b=0.96

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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 derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.