Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C Ax (BUC) = (A x B) U (A x C), that is, (x,y) = A x (BUC) = (x,y) = (A x B) U (A x C).

Q: f' (æ) =Vx+, f(0)=2 f"(x) = 3x² 16x + 16, f'(0) = 1, ƒ(0)

A: Topic:- application of integration

Q: 9. y = 3 Arcsec 3x

A: On solving this we will get

Q: (a) √738(t - 4)dt (b) 738(t + 2)dt (c) √²38(t+4)dt (d) f²3x²8(t-4)dt (e) ¹3x²8 (t+2)dt -3 (f) ²3x²8…

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Q: COS cos t 1 - sin t - dt

A: To evaluate: I=∫0π2cos t1-sin tdt

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Q: 5TT Convert the polar coordinate 9, 3 X = y = to Cartesian coordinates.

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Q: 15. y=Arccos (x²)

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A: Solved below.

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Q: Find the area of the region bounded by the curves y = x²y = x² and ² 01/2 02 O 1/3 O 2/3 = xy = x.

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Q: What is the mass in both (a) slugs and (b) kilograms of a 4390-lb car? Answers: (a) m = slugs (b) m…

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Q: ind A or each of the following intervals, tell whether f(x) is increasing or decreasing. -∞o, A):…

A: Topic:- calculus

Q: Q4: If f(x,y) = x²y +exy Siny Find 1) 2) (D = f) po Po at po(1,0) in the direction of 0 =

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Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: 3. Find the equation of the tangent lines and the normal lines to the curve y = √2x-1 at x=5

A: As per the company guidelines we are supposed to answer only first question. Kindly repost the other…

Q: What integration technique can be used to integrate: Integration Formulas Trigonometric Substitution…

A: Solution is here

Q: . y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: Q1:Discussion a continuity of the function f(x,y) sin x (x, y) = (0,0) f(x, y) = x (x, y) = (0,0)…

A: To find whether given function is continuous at (0,0) or not.

Q: (c) Show that the function is a solution of the differential equation (−1)" x2n f(x) = Σ (2n)! n=0…

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Q: Find the general solution of the following 2nd order differential equation: y* +2y + 2y = 0

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Q: iv) in complex number z³. (z)² = |z|².z

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Q: (e) 2a7/2.a¹/2 a-1 (f) √₂√b a 5 √ab

A: As we know the Rules of Exponent or Laws of Exponents . 1). ax·ay=ax+y 2). ax÷ay=ax-y 3). axy=axy…

Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: Find the solution of the following differential equation. (x² - 1) + 2y (x + 1)² dy dx 1.

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: To find out the volume of revolution.

Q: ·S. Given : 1 value of -AB AB. 3 72 40 8x + 1 20 3 280 3 4x - 3 4x - 3 dx. If we let the…

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Q: and

A: We have to find the solution of the given differential equation

Q: Find the integrals of the given in the picture

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Q: The position of an object moving along a line is given by the function s(t)= - 8t +72t. Find the…

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Q: The current population of a small town is 3947 people. It is believed that town's population is…

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Q: d²y dy 4. (a) Compute the general solution for: +4 dt +3y=e-t/2. dt² (b) Compute the solution with…

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Q: Consider the function f(x) exact values. f'(x) = f''(x) = f'''(x) = = Compute each of the following.…

A: Topic:- derivatives

Q: Which of the following is not an improper integral? # of th al

A: We know that, An improper integral is a definite integral that has either or both limits infinite or…

Q: Question 5 What is the amount of work done on a spring when it is compressed from its natural length…

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Q: Q1: Find the for the following functions: dy dx 1- y = e(x+In 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh…

A: 1)y=ex+ln(5x) 2)y=cosh-1sin2x 3)y=xsinhx

Q: (c) 2x2(4x6)2 (d) (3x-2)-4-4

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Q: (e) Use any test to determine whether the series is absolutely convergent, conditionally convergent,…

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Q: 8 Find the area bounded by y y = 2x, y=0 and x = 3. X Using vertical element, what is the integral…

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Q: Scotch is looking to make a larger size roll of duct tape. The current roll is shown in the photo.…

A: First finding the volume of original roll

Q: .2 (a) x² + y² (b) 3x2 + 3y

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Q: fz² dz along the indicated paths: -1+i -1 C 0 (a) 1 1 + i 17 0 (b) 1

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Q: Q2: A. Determine if p = 1-3k and q = 61-3j-4k are parallel, orthogonal or neither. B. Find the…

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Q: Find the general solution of the differential equation: y' - 5y = te-2t Use lower case c for the…

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Q: Calculate (31-2). 051 0142 743

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Q: Derive the formula for trapezoidal Rule to evaluate f f(x) dx

A: The trapezoidal rule is to find the exact value of a definite integral using a numerical method.

Q: 5. Evaluate using the circular disk method. Find the volume of the solid formed by revolving the…

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Q: 19 A curve with polar equation r = 8 sin 0+17 cos 0 represents a line. This line has a Cartesian…

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