3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: To evaluate the value of  ∫-∞∞7x2+4x+8dx=7∫-∞∞7x2+4x+4+4dx=7∫-∞∞7(x+2)2+22dx

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Sh dx

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: 4х Consider the function A(x)=2x+ for x > 3 Зx-1 (a) This function has one critical value larger…

A: We will start from critical points and follow upto inflection point

Q: dx 00 2 X х +4

A:

Q: Investigate the convergence of the following series. H.' 2n+5n 2) ΣΗ-1 ILJ! 3n

A: Here, the given series is: ∑n=1∞2n+5n3n Let, an=2n+5n3n; n≥1

Q: Find the second derivative of the function x2y – 2 = 5x + y

A:

Q: 1+tan-1x D. y = + sec-1xcsc¯1x + xsin-1x +V1 - x2 2-3tan-1x

A:

Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: 24) Find the maximum rate of change of at the given point and the direction in which it occurs.

A:

Q: Find the indefinite integral and check the result by differentiating. Determine an appropriate…

A: Solve the given intregal

Q: 7. If ā = -i+ 3j + k,5 = 31 – 2k and ĉ = 2î – † + 4k, determine 2(ã +5 – 2€) – (35 - 2)

A:

Q: de (x+2) h+2+ +C (r+2) x + 2- Option 1 Option 2 In Ix + 21 + 4r+5 + C in x + 2 (e+2) O Option 3…

A:

Q: Find the generating function for this when n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5,…

A: Given :n=2, f(2)=1. n=3, f(3) = 6. n=4, f(4)= 25. n=5, f(5) = 125. n=6 f(6) = 750To find : The…

Q: Calculus Question

A:

Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

Q: Solve for x in the following expression using the quadratic formula. 3x2 + 19x – 4.9 = 0 Use at…

A: We can solve this as follows:

Q: 2r³ – 4x² – x – 3 dr x² – 2x – 3

A:

Q: x3-4x-10 dx. x2-x-6 (2x + 2 In|x – 3| - 4 In |x + 2|) + C - 2 In|x – 3| + 4 In |x + 2l) + C Option 1…

A:

Q: Consider f(x) = 6.9x3 + 9.1x2 - 4x + 7.7. Using the given function, approximate f(4) by making use…

A:

Q: Sins 느 x Uos

A: We need to evaluate integral.

Q: पेरडा test conerg ence and divergence

A:

Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: 3. Evaluate (D +x)(D–x). Note: D=- (denotes derivative with respect to x). A) D²-x² B) D² -x² - 1 C)…

A:

Q: Diego knows that 82 64 and that 4° = 64. What other statements are true? O V64 = 8 O V64 = 4 O…

A: We can find the true  statements as below.

Q: Evaluate the following indefinite integral: x dx 1.) S- Vx4 - 1

A:

Q: is an angle in standard position, tan(e) 0, then the terminal side of lies in which quadrant? A IV…

A:

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: Fill In The Blank Refer to the given below. Find the indefinite integral. Simplify your final…

A:

Q: Find dy/dx. x = Vt y = 9-t dy dx

A:

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A:

Q: The most conveneient way to evaluate x2- by substitution is to let Vx2- 4 =y A True B) False

A:

Q: Write the expression as a single Integral 1. f f(x)dx + f(x)dx =, 2. S f(x)dx – , f(x)dx = 3. f…

A: Use the property of the definite integral; 1). ∫abfxdx=-∫bafxdx 2). ∫acfxdx=∫abfxdx+∫bcfxdx   1).…

Q: 2x (x- 3)2 .

A: Given: ∫2xx-32dx

Q: Find the general solution to the following equations. dx dy 1. + y = x , = 3y dt dt

A:

Q: 17. y dx — (х + бу?) dy %3D 0

A: To determine the solution of the given differential equation.

Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x, y)= 2x² – 3y –…

A:

Q: A function is defined as f(x) = x3 - x - 11 = 0. Between the interval [2,3] find the root of the…

A:

Q: ind [r(t) · u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = ti + 5t2j + t³k, u(t) = tk (a)…

A: Solving

Q: Find the positive root of the equation x - 4x + 9 = 0 in the interval [2,3] using Regula Falsi…

A: We will check weather at x=2 and x=3 function have opposite sign. If sign is not opposite than there…

Q: Verify Green's Theorem by evaluating both integrals ам y? dx + x2 dy dA ay for the given path. C:…

A:

Q: x² – 2 (x + 2)(x + 1)²

A: Partial fraction

Q: Find the general solution of y'' - 2y' - 8y = 24(x2+1)e4x by using VARIATION OF PARAMETERS

A:

Q: Find the positive root of the equation x + 2x2 + 10x - 20 in the interval [1,2] using Regula Falsi…

A: Let, the given function be: f(x)=x3+2x2+10x-20 And, the formula of the method is:…

Q: 1. Find the angle between the following two vectors. and

A: The given vectors,  8,-5 and -9,-7

Q: '글 +2+글 +5 The sum +8+ +11 written in sigma notation is equal to 8 3k-2 A k=1 2 8 3k - 1 B k=1 8 3k…

A: The sum 1/2 +2+7/2 +5+13/2 +8+19/2 +11.

Q: The progress of a person on a long hike is shown in the graph. 9. D 8 - 7- 6 - B 2- 1- 5 7 8. Time…

A: The given graph is distance against time ,  where distance is marked on y-axis and time marked in…

Q: What is dy/dx for va+y+ Vay = 6?

A: Given problem:- What is dy/dx for √(x + y) + √(xy) = 6 ?

Q: (ye» dy Ans. (3e* +1) 4 11. 0

A:

Q: x-4 dx x2+2x-15 1 -In]x + 5 - Inlx - 31 +C 9 In|x +5|- In|x – 3| + C Option 1 Option 2 Ln x + 5)이 1…

A: Given problem:-

Q: Use a change of variables (Substitution Method) to evaluate the following definite integral. Show…

A: