(b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

Q: B-Find the area of the region inside the curve r-1+cose and outside the curve -1 and graph the two…

A: Equate both equations to find limits and intersecting points of these curves

Q: 100 The value of p for the series Ση=1 2n | n! by using ratio test is -1 8 N 2 0 1 O

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Q: Solve the given initial-value problem. The DE is homogeneous. 3 xy² dy = y³ y -x - x³, y(1) = 3

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Q: The angle between the two vectors is not equal to Select one: O True O False u= and v= 0= π

A: Here we use the concept of dot product of the vectors.

Q: In x dx

A: Solution:  Step_1  :       ∫ln x dx we will solve it by using integration by parts method.

Q: The z-transform of [n] = u[-n] is

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Q: S In (x) √xln(x)-x =dx

A: Please see the below picture for detailed solution.

Q: Question 2 [ Given the equation -5x² + 30x - 5y² - 10y - 5z² - 90z = 21 a) Show that the given…

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Q: Find the roots of: (D² - 4) (D2)y = 0

A: To find the roots of the given equation D2-4(D-2)y=0

Q: Matrix has only one row call Row Matrix. multiply a matrix (A) by another matrix (B) if the number…

A: We check the given statements are True or False.

Q: 3. I Graph of f Graph of g The graphs of the functions f and g are shown in the figures above. Which…

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Q: Choose the angle (in radian) between the follow u = and O 3.142 O 1.047 Од None of the others O…

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Q: 6. Which of the following is FALSE? 7. f A. (4 cos x-3 sin x) dx = 4 sin x + 3 cos x + C B. f3e³x dx…

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 8 O 6 None of them O 2 O 4 O

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Q: 6. Which substitution can work to compute for the indefinite integral fx√√x + 5dx? A. u=x C. u=x+5…

A: we use substitution method to  find the value of integral

Q: (1) Suppose directional derivatives of the scalar function f(P) at a point P = (x, y), in the…

A: Solution: Let ∇f=xi+yj Then ∇f.3i+4j5=1⇒xi+yj.3i+4j5=1⇒3x5+4y5=1⇒3x+4y=5............(1)

Q: Using Linear Coefficients of Two Variables, solve: (2x - 5y + 3)dx - (2x + 4y - 6)dy = 0

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Q: 1. Determine the dot product of the two vectors in the diagram.

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Q: The geometric representation of the equation is a circle in R3. Select one: O True O False -3x²-3y²…

A: Given: -3x2-3y2=-18

Q: 2" The value of p for the series En=1 by using ratio test is n! -1 O 8 2 0 ( 1 O

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Q: The particular solution (yp) of the equation y" - 3y' + 2y = 5 e* is yp = -5xex False True O

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Q: True or False: We have Select one: O True O False 8 So vid 0 √xdx = 12.

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Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

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Q: On the moon, all free-fall distance functions are of the form s(t) = 0.81t², where t is in seconds…

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Q: B-Find the area of the region inside the carver-1+cose and outside the curve -1 and graph the two…

A:

Q: S In (x) √xln(x)-x -X dx

A: ∫ln(x)xln(x)-xdx

Q: Please solve the bottom question.

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Q: (g) y dx = (y - xy²) dy Oseparable exact linear in x linear in y Ⓒhomogeneous Bernoulli in x…

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Q: Q2\ Choose true or false from the following sentences:- Matrix has only one row call Row Matrix.…

A: 1- true Matrix having 1 row is called row matrix.  2- true.  Gauss Jordan method is used to find…

Q: Evaluate 4 1 2 (Nat 13.402 - -13.402 13.042 • Vx + 3 3 X 4 | -13.420 +18 -1.3204 4 X None of them 4…

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Q: The area enclosed by one petal of the polar curve r = cos20 is False True O

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Q: I sin²(x) cos(x) dx

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Q: Question 2 Given the equation -4x² + 40x - 4y² - 32y - 4z² +24z = -200 ] Show that the given…

A: We find center and radius of the following sphere.…

Q: 20) If 8 is an angle with terminal side in 4th quadrant such thatv tan 9 = a) O b) O c) O d) O then…

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Q: F(x)=5cos(3x) on [-pi, pi] What intervals is f increasing and decreasing?

A: F(x)=5cos(3x) on [-pi, pi] What intervals is f increasing and decreasing?

Q: Which of the following is the area of the region bounded by the function y = x ^ 2 the vertical…

A: To find area of the bounded by the function.

Q: Find the volume of the solid whose base is a circle with radius 12 that has cross-sections…

A: Recall that the volume of a solid, if the cross-section is perpendicularto the x axis, and its area…

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Basic partial derivation is used.

Q: Find the mass of the portion of a sphere in the first octant with radius 1 and density function…

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Q: The angle between u = 3i- j - 2k and v= i + 2j- 3k is O 60° O 30° 180° 45° 90° O

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Q: The graph off-1 is given below. Graph the tangent line to f-1 at the point P(1, 1) for f(x) = -x³ +…

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Q: A book is to contain 36 in² of printed matter per page, with margins of 1 in along the sides and 1…

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Q: -0.1 0.9062cos (1-√√3x) d x 吧。 (1-√³x)]" [sin (1- sin (1-√√3a) - sin (1-√√3(-0.1)) sin (1-√3a) 1-√3a…

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Q: If w = f(r,s,t), r = x-y, s = y - z, t = z - x then dw Əw + ?х -1 Əw дz 0 о II 1 -2 ( 2 O

A: Given the function w is function of variables r,s and t . further r, s and t are the functions of x,…

Q: = Find the volume of the parallelepiped determined by the vectors a c = (2, 3, 1). Volume =…

A: The volume is given by scalar triple product of vectors.

Q: Find the general solution of the given differential equation. 3 +24y = 8 dy dx y(x) = Give the…

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Q: Simplify:- 16--// 5 2

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Q: A 100 ft wire is attached at it's end to the tops of two 50 ft poles that are positioned 90ft…

A: Concept: Catenary curve: A flexible hanging chain or cable is shaped like a curve in mathematics…

Q: (h) x. yexy - x dx separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y…

A: