Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

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Q: Show that the average value of sin^2t over [0,2pi] is equal to 1/2. Without further calculation…

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Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: y = log (cos(2x) );y'=* %3D %3D O 2 tan ( 2x ) / In (10) O - 2 tan ( 2x ) / In (10) O 2 cot ( 2x ) /…

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Q: Question 7 Find the partial derivative of z with respect to x 8: da = -2x (3x²+1) sin(x²) + 6xcos…

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Q: Question 1 π 2x Evaluate the integral cos(xy)dydx 4

A: ∫45∫0π2xcosxydydx

Q: 2 S (x) + x³)dx = ? -1

A:

Q: The current I(t) in an LC series circuit is governed by the initial value problem below. Determine…

A: In this question, we solve the initial value problem by using the Laplace transform and properties…

Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: Question 4 (а) Evaluate, with the order of integration being reversed, an equivalent integral of the…

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Q: Evaluate in terms of gamma function: x°e-3¤ dx O r(7) Or(17) O(7) OI(7)

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Q: a n п i = 6 dz EVALUATE IN TERMS OF GAMMA FUNCTION.

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Q: 1 Find the mean value over the interval [0,2n]. 4+cosx

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Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Question 2 > The function ` f(x) = (5 x-9)e^(-6 x) ` has one critical number. Algebrically use the…

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Q: Question 7 Determine if h (z) = –- is continuous at x = 1. (Show your solution at your bond paper.)…

A: hx=x-1x2-1

Q: Find the average power of the signal: x(t) = cos x + sin x %3D

A: Given: To find the average power of the signal: x(t)= cos x + sin x

Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: Question 8 Suppose that a biomass B(t) changes with respect to time t (hours) at the rate dB Vt +…

A: We have to find

Q: 2) Give a big-Oh estimate, O(x³), for the function f(x) = (1 + 2x + 2cosx + 2r*)(log x² + 3lx| + sin…

A: 2 Given function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx. We have to estimate Ox3 and determine the…

Q: 6) Using gamma function, evaluate So 6 хе 2x dx

A: Introduction: Gamma function is an integral function that is defined through an integration. The…

Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

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Q: Problem 3 Use part I of the Fundamental Theorem of Calculus to find the derivative of…

A: Given:

Q: Question (1) Find the Following Integ (1) S(x? 1 +3) dx (2) S

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the average power of the signal: x(t) : = cos x + sin x (-7/4, 0) (7n/4, 0)

A: From the given graph, it is observed that the period of function is T0=7π4--π4=2π. Compute the…

Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

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Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

Q: Question 6. Evaluate the indefinite integral 1 - dx. J x(x² + 2x + 2)

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Q: QUESTION 4 witQUTMOUTMOU with respect to r. Differentiate y 3- cosh r 6+ sinhr MO

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Q: Question 8 Integrate the function. dx V9 - x2 COs:1 X+C 2 cos x+ sin x+C D sin *-C Question 9 413

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Q: Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii)…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: | Example 8.11. Evaluate the integral the error with the exact value. dx using Simpson's 1/3rd rule.…

A: Please find step by step solution below

Q: 5. Evaluate by using beta function: | °(1 – r*)} dx.

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Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

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Q: Question 18 Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+…

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Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: Question 4. Evaluate the following integral. |(r3 + 4)°3x dx

A: ∫x3+423xdx=∫x32+2x3(4)+423xdx  [expanded the square]=∫x6+8x3+163xdx=∫3x7+24x4+48xdx [distributed the…

Q: Question 38 The critical point of f (x) = (sin x) (cosa) on the interval (0, π/2) is at x = Ono…

A:

Q: 5) Give a big-Oh estimate, 0(x³), for the function f(x) = (1+ 2x + 2cos x + 2x2)(log x² + 3|x| + sin…

A: 5 Given that the function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx......1. We have to estimate Ox3 and…

Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: Question 4. Given the function v(2) = In(3 + sin(4z)) %3D and-the mesh = zo+ ih. where zo determine…

A: We are entitled to solve only one ques at a time and up to 3 sub-parts only. Given - Given the…

Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: Example 1 Differentiate each of (a) f (x) =2 x' cosh x sinh t (b) h(t)=

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Q: Question 3: Find the integrali(using u-substitution) Ses (8x+1) dx

A: To evaluate: I=∫cos (8x+1) dx

Q: The definite integral from 0 to = of cos x sin xesin² x dx is 4 O e - 1 e+1 e-1

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Q: Question 2: Use the Green's theorem to solve $(v² +3x² \dx+2xdy which bounded by x=0,y=0 and 4(x² +…

A: We find the given integral by using Green's theorem.

Q: Given that ſ♫ sin xdx = 2, find the average value of the sine function on the interval [0, π]. Also,…

A: Please see the below picture for detailed solution .