b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S x²+2x+1 x-2

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: B. For the figure shown below, find the sum of the areas of all the semicircles. 244

A: Using formula of area of circle

Q: Determine whether the improper integral is convergent or divergent. 33) S ∞ dx x2/5 0 A) Convergent…

A: We know that integration of xn   is xn+1/n+1.   Here i attached the solution of this question.

Q: The graph shows the parabola c(z) = 7-², together with a shaded region. 94 -2 -1 3 + -2 Set up the…

A: The given equation of the parabola is: cx=7-x2 Now find the x-intercept of the given parabola.…

Q: ib Show that the function defined by F(x, y) xy √² + y² O is not differentiable at point (0,0) if…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: x+1 2-1 24 - 1 Evaluate the given limit of lim O-1 01/1 0 -¹ O Olimit does not exist if it exists.

A: Solved below...

Q: Complete the table after finding a simplified form of the difference quotient. 5) For the function…

A: f'(x) ={ f(x+h)-f(x)}/h

Q: Let A(z) = f(t)dt where f is the function given by the graph below. 3- 2 + 2 H d -2 A(3) - A(8) -

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Q: 3.4, 4.1) 1. Let f(x)=x²+2x+10. (a) Find the average rate of change of f with respect to x on the…

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Q: 35. √2x³ = 9x³ - 3x + 1 x³ = x² dx

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Q: 5. If f f(x) dx = 12 and f f(x) dx = 4, then all of the following must be true a. f f(x) dx = 16 ✓…

A: topic- definite integral

Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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Q: Evaluate the double integral over the given region R. xy² dA 2 X + 1 R xy² SS. dA= +1 R (Type an…

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Q: Work through the following steps to evaluate S. ( (x² + 4) dx. a) We know that a = and b = b) Using…

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Q: find the centroid of volume if the volum is equal to 7/15 π

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Q: Given the graphs determine the integral to find the volume, if it is rotated about the x- axis (1,…

A: We have to find the volume.

Q: Solve the following second order differential equation, clearly showing all calculation steps d²y dy…

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Q: a. Interest is compounded quarterly b. Interest is compounded daily c. Interest is compounded…

A: Follow the procedure given below.

Q: Find the divergence of the following vector field: 0 O 2z O O F = (y, -x + z², 3x)

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Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y - 2 = 0…

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Q: Determine the thirteenth term in the sequence whose nth term is an= -6n a. -66 b. 19 c. -78 d. 94

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Q: √√3+ rdr then 0 (2)=√√3+230 I X

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Q: 1. f(x) = cos (-:-)

A: From graph, it is clearlimx→∞cos1x =limx→-∞cos1x = 1

Q: 32 Evaluate the integral ·ƒƒ(6-y²) dy dx. 00 The value is 18. (Type a simplified fraction.)

A: We know, ∫xndx=xn+1n+1, for any real number n.

Q: Complete the Proof Statements Reasons 1. ABCD is a AC BD given 2. AD BC 3. 4. LABC = ABAD 5 ZDAB…

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Q: Evaluate the following integrals: 1. f(cos x + csc² x)dx 2. f(tan x + sec² x) dx 3. (1+sec² x) dx…

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Q: Consider the function. f(x) = Identify the domain off. (Give your answer as an interval in the form…

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Q: Answer the following. Complete Solution 1. Integrate -2 ex sinx a. dx 0 1+x² 62e

A: F = ∫02exsinx1+x2dxIt is a complex integration hence, numerical method is used.…

Q: In your own language, describe the pattern of the following sequences (The sequences are given as a…

A: We draw required connection between the pattern and formulas as below.

Q: [1 1) If A = 3 15 2] 4 6] B = [-3 -21 -5 314 4 253 3. [P 91 Find: D = r s tu

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Solve - cos2 - sin²x = 1 on the interval 0 < x < 2T. O 3π 2' 2 O no solution O 0, T O 0, T, 2T

A: The given equation,    -cos2x-sin2x=1 on the interval 0≤x≤2π

Q: Evaluate the integral. π/4 Jo 0 sin5(x) dx

A: Given query is to find the value of the integral.

Q: Find the position vector for the vector v, whose initial point is (0, −2) and terminal point is (5,…

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Q: Question 13 Which of the following satisfies the differential equation d² y dx² A. y = e³r B.y=e-3x…

A: Explanation of the answer is as follows

Q: a) Find the area of the region enclosed between the curve y = x² and the line y = 4x. b) Find the…

A: The objective is to find the area .

Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (7x²2) to…

A: Maclaurin series of sin(x) :              sin(x) = x-x33!+x55!-x77!+...

Q: In APQR, p = 6.7 inches, r = 2 inches and /R=142°. Find all possible values of ZP, to the nearest…

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Q: π I Find the volume of the region bounded above by the surface z = 7 sin x cos y and below by the…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(In(5t)) dt t

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Q: Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² +…

A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1

Q: Find the divergence of the following vector field: 00 O 2z O F = (y, -x + z², 3x)

A: We can solve this as follows:

Q: Find the area of the region between the graphs of y = 16-2² and y=-62 +9 over the interval -3 ≤z≤1.…

A: Given: y=16−x2 and y=−6x+9 Let's first find the intersection point of y=16−x2 and y=−6x+9 16-x2…

Q: Calculate the area contained between the curve y = cos x, π<x< , and the line y =

A: Given:-y=cosx, -π&lt;x&lt;πy=1/2

Q: Find the general solution. ورم

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Q: On the coordinate plane below, sketch the position vector (0, 3). PENCIL THIN BLACK

A: solution:-sketch the position vector 0, 3

Q: Determine the equation of the hyperbola with center (8, −5), a vertex at (8, −2), and a co-vertex at…

A: The objective is to determine the equation of hyperbola.

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

A:

Q: arbor during a certain 24-hr period is approximated by the function 2]. + 7.9 (0 ≤ t ≤ 24) esponds…

A: The rare of change of a function f(x) at x=c is f'(c)