(a) Verify that tanh P-tanh Q 1-tanh P tanh ọ tanh( P – Q)

Q: Refer to the given function below to answer the following questions: dr 0 de 2 = COS-

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Q: Which integral below gives the volume of the solid of revolution obtained by rotating the bounded…

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Q: H.W // find the integral _1=√15 e-x³².dx. using 7. dx. using two and three points of Gaussian -1.5…

A: In numerical analysis, the Gaussian Quadrature method approximates the definite integral of a…

Q: 10 Σ (3n – 1): 125 n=1 10 Σ–1 (3) -1, 125 Σ (3n – 4): 125 10 Ο Σ(3n – 4): 125 Ο Ο O e Θ

A: Verify all the option   then find the sum.

Q: Find the area bounded by : f (x)=e*, g(x) = e¯* and x=3. A (e³-1)² e³ sq. units (В) (e²+ 1)² e² Ⓒ…

A: The region is bounded by fx=ex, gx=e-x and x=3

Q: Find the linear equation of the given below using any of the 3 methods. Show your solutions here. X…

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Q: 1. Find the area under the curve y = x² from x = 1 to x = 3. -y-x² (1,1) x-1 (3,9) x-3

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Q: 1. x + y + xy = 21

A: We will use simple differentiation rules to solve this question.

Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

A: A critical point is a point where the derivative of the function is 0 or does not exist. At critical…

Q: √__(x+1) dx (x+2)(x-1)² 1 9 3 2 0-11/11 - 01/17 9 3 2 3 1 2 9 3 -io 1 9 - = 1[ A B + x+2 x-1 + C…

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Q: Question 3 Iff is continuous on [a,b], then T True F False b then f(x)dx = f(x)dx T a

A: Here it is given that f is continuous on [a,b] From the integration we can take the constant value…

Q: The length of a rectangle is given by 4t - 3 and its height is √2t, where t is time in seconds and…

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Q: .b if f is continuous on [a,b], and f(x) 20 then √VF(x) dx = f(x) dx T True F False

A: Topic: application of integration

Q: Determine the area bounded by f(x) = x² — X and x-axis. 1 A -unit² B -unit² Ⓒunit² 2 Ⓒ -unit² 1

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Q: How many antiderivatives does a function of the form f(x) = x^ have when n*O? A may vary depending…

A: To write down the number of antiderivatives a function can have.

Q: L(sin 2t cos 2t) Your answer

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Q: S Given 1 хр for which the improper integral converges? A {0,1} (B (1,00) C (-∞0,00) D (-∞,1] dx,…

A: The given improper integral is: ∫1∞1xpdx Suppose p=1 then: ∫1∞1xdx=ln x1∞=∞ So, diverges.

Q: = 4 R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

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Q: That statement "We can use the General Power Formula of Integration for indefinite integrals…

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Q: B S₁ Evaluate: A In 10 (В) ® -log² (x+1)+C 2 In 10 In[log(x+1)] + C -In 10 log2 (x+1)+C 2 D dx (x+1)…

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A =C sin x sinx cosy…

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Q: Initially 80 grams of radioactive substance was present. After 4 hours the mass had decreased by 6%.…

A: Let's find amount remaining after 40 hours.

Q: tan (3x) lim x→0 sin (2x)

A: Given query is to find the limit of the expression.

Q: Show if the following limits produce an indeterminate form. Then, evaluate the following limits. lim…

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Q: evaluate the limit and simplify. Complete solution.

A: Evaluating the limit

Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: Which of the following methods can be applied to find a particular solution yp of y" +y = cos(ex)?…

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Q: (D) 1

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Q: A car is travelling at the rate of 88 ft/sec when the brakes are applied. The car begins to…

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Q: Determine the integral: x²cosxdx A x²sinx+2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C Cx²sinx +…

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Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3. (e³+ 1)² A - sq. units (e³-1)² sq. units e3…

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Q: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

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Q: Question 32 dx Evaluate: (x+1) log(x+1) A) -In 10 log2 (x+1) + C 2 B --log² (x+1)+C 2 In 10…

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Q: lim (lnx) = . x →+∞

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Q: Write TRUE or FALSE before each statement. Solve y + y = ry³. Statement 1. The integrating factor is…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: The improper integral A 1 B 0 C St edx is

A: To solve the improper integration.

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: To find the work done.  Option D is correct.

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1 (A) 1 unit² B -unit² 3 -…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A: To find the volume of the solid.

Q: Q/IF 3 = sin(x) 0²³²141 y= (4) y = 3/2 I sin(x) cos(x) Prove that

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Q: Evaluate [C sin(x + y)dxdy. Answer: 0

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Q: Q/IF 3= sin(X) (²314) y = 3² sin(x) cos(x) Prove that

A: To find y':

Q: formula for the sum of the first n terms of a geometric sequence to find the sum of the first 11…

A: Given query is to the sum of the 11 terms

Q: We can apply General Power Formula of Integration on which of the following integrals? A…

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Q: Which of the following can be determined given A √ ² (f(x) + g(x) + h(x)) dx 4 ® [ g(x) dx ©…

A: We have given the Integration values of function f(x),g(x) and h(x) on a certain interval. We want…

Q: (x+1)dx (x+2)(x-1)² S A 2 - x+2 B -1 + (x-1)2 ]dx. the values of A & C respectively are:

A: integration

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: A detailed solution is given below.

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: If a function F is an antiderivative of the function f then F'(x) = f(x) , and ∫f(x)dx=F(x)+C for…

Q: Which of the following can be determined given Ⓒ [² (4f(x) + 9h(x)) dx 3 ® √²³((x) + B © ²(f(x) -…

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