Evaluate the limit 3(y²1) lim y 4 7y²(y-1)³

Q: Determine the volume generated of the area bounded by y=√√x and y=- (A 128/15 (B) 112/15 Ⓒ136/15 (D…

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Q: Find the value of k for which the constant function (t) - =k is a solution of the differential…

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Q: Q2: The equation of the tangent line to the graph of y=r2 and t=4x² at t=1 is (not that x is…

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Q: fx arccos x dx 2.

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Q: 1. Evaluate the given integral Q. ry+1 ry+z Q= 0 0 xyz² dx dz dy

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the area contained between the two curves y = 3x - x² and y=x+x². 71/6 81/5 91/4 62/3 None of…

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Q: Question A particle moves along a line with a velocity v(1) = 3√1-4, measured in meters per second.…

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Q: At 12:00 noon, there were 200 bacteria present. By 4:00 pm, there were 379 bacteria. If the bacteria…

A: At 12.00 noon, there were 200 bacteria present.By 1:00 pm, there were 379 bacteria.

Q: Q/Find the Taylor Polynomials of orders 0,192 and 3 generated by fat F(x) = Sinx 29=0

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Q: 8 3) If f(x)= 2 (x-1)*, then f (2) (1) = Σ k=0 a) b) 2 c) 4 d1

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Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

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Q: Problem 1: Determine centroid Y-bar with respect to the x-axis. A = 1.6 m B-3.9 m V A A B B

A: We have to find the centroid.

Q: 2) Sketch the solid whose volume is given by the integral  and evaluate the integral. ∫0 to pi/2 ∫0…

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Q: A thermometer reading 75°F is taken out where the temperature is 20°F. The reading is 30°F 4 minutes…

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Q: N IS. Use the graph to answer the following questions. (a) Over which intervals is the function…

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Q: Evaluate the integrals. x√√1-x² dx a. x X b. I si sin5 -cos-dx 3 3

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Q: Solve y'' - 2y' + y = 0, y(0) = — 5, y'(0) = = y(t) = - 8

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Q: Using 1/3 or 3/8 simpson rule, find the area or volume bounded by the given curves,axes and/or…

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Q: 5. For the below ordinary differential equation with initial conditions, state the order and…

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Q: dy at t= is (not that these functions in N) dx a) -1 b) 0 c) d) 1 e) others Q5: If y=tant and x =…

A: The objective of the question is determine the derivative at given point and choose the correct…

Q: Q1: If y=sint and t= sin x, then at x = a) 0 b) c) cosl dx² d) -cosl e) others

A: I have stated the used properties in the solution

Q: 2- Explain why the following linear systems are positive definite, then solve them using the…

A: answer is in next step

Q: 3. Find the inverse of the function: ƒ (x) = 4x² − 5

A: The answer is given below:

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Solution: L-1 {1/s7}

Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Δy ~

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Q: 3. For the below ordinary differential equation with initial conditions, state the order and…

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Q: Use polar coordinates to evaluate: a) SSRdA/(x²+y²+1) where R is the region in the upper second…

A: The value of the given region is (π/4)ln(2)

Q: 1. 2ydx+x(x² In y-1)dy=0

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Q: Use the Laplace transform to solve the given initial-value problem. y" + y = √2 sin(√2t), y(0) 13,…

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Q: Q4: Let y = √t and a) 2 b) 3 c) 4 t = x² then y(") = 0ifn= d)5 e) others

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Q: √√9-y² 9 = L Q (2x2) dz dy dx Зг 2. Give the (upper, lower, lateral) boundaries of the solid S of…

A: simple integration are ...

Q: You are building a cylindrical barrel in which to put Dr. Brent so you can float him over Niagara…

A: Given problem:- You are building a cylindrical barrel in which to put Dr. Brent so you can float him…

Q: dx (4+x²)² √

A: Explained below

Q: Find the area of the region bounded by the parabola y² = 2x2 and the line y = x - 5. 16 17 18 19…

A: Given: y2=2x-2 and y=x-5 Now find the point of intersection between the given curves. y2=2x-2 ;…

Q: When a homeowner has a 25-year variable-rate mortgage loan, the monthly payment R is a function of…

A: We have to interpret the above term.

Q: Q1: If y=sint and t= sinx, then at x = a) 0 b) c) cosl 2 dx d) -cosl e) others

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Q: - (f* (t² + 1)¹⁰0 dt)" dt - Some ₁ tanx 1 + t2 d. y = e. y =

A: According to Leibniz integral rule : ddx∫a(x)b(x) f(x)dx=fbxddxbx-faxddxax

Q: Evaluate dy/dx using implicit differentiation.

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Q: Evaluate the integrals. -32 a. S x-6/5 dx 1 -π/³1 - cos 2x b. 2 -TT/3 -dx

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Q: II. Coefficients Linear in Two Variables 1. (6x-3y+2)dx-(2x-y-1)dy=0 2. (9x-4y+4)dx-(2x-y+1)dy=0

A: We can solve the given differential equation.

Q: A Ferris wheel has a radius of 12 m and rotates once every 16 seconds. Suppose a passenger boards…

A: We can use cosine equation to solve the question

Q: -1 L 1 s2 + 2s

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Q: use your calculator. 3 -2 7 8 -2 2 - 4 -12 7 0 4 3 4 7 4 7 2 8 7 -2 3

A: det3-2478-2-2047444-247-1237-2874-23Reduced echelon form is,=det…

Q: -S² √√x" dx -2- ។ (X) 5 JX dx -2

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Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: 15. Find the inverse of matrix A. A = 38 26

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Q: xy h) log₂ = Z i) log2 (2/2) =

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Q: Find the directional derivative of f(x,y)=sqrt(x²+y²) at P(4,- 3) in the direction of μ=[8,-15].

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Q: Exponential and Logarithmic Functions 11. Use the properties of logarithms to fully expand the…

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Q: 57. If f(x) = (A) (0,00) fen²x + (n (ex) (n² (ex) dx; f(1) = 0 and g(x) = 1 -f(x). Then the domain…

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