Differentiate with respect to t. y = d cos(t) + t² sin(t) y'- sin d( 2t + d) + t²cos (t)

Q: Find the Particular Solution: y(x-6y)dx-x(2x-9y)dy = 0; when x=1, y=1 a. y²(y+3x) = 3x² * b.…

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Q: Solve the following system of inequalities 2x+y-8>0 3x-y+6>0

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Q: x Let a and b be positive real constants, and let y = f(x) such that tan ay statements is TRUE? O dy…

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Q: f(x) = 9x²

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Q: Which of the following statements is/are ALWAYS true for a function f and a real number c? A: If lim…

A: We can answer the question as below.

Q: a) Let zi = 4 cos Find 2₁ - 22 and 7π 12 21 Z2 5TT 12 + i sin and = 3 (cos. Leave your answer in…

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Q: Find the volume of the solid generated by revolving the region bounded by y=3/(2√x), y=0 & 1s XS4.

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Q: For numbers 4-5, consider a plane bounded by the curve x = -y² + y +2 and the y-axis. The…

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Q: Consider the two by two system of linear equations a) Use the method of substitution to solve this…

A: Given :x+3y=75x+2y=-4

Q: Which of the following is NOT true about the curve * y = x3 – 5x2 + 2x+8? (-1,0), (2,0) and (4,0)…

A: The given function is: y2=x3-5x2+2x+8y=±x3-5x2+2x+8 If a function is symmetric with respect to the…

Q: Given than [(x) f(x) dx = 7 and f (x) da = -5, which of the following is NOT TRUE 6 ® [f(x) dx =…

A: Given that ∫-23fx dx=7 and ∫36fx dx=-5, then to determine which of the following is not True.A…

Q: A ladder 25 ft long rests against a vertical wall. If the bottom of the ladder is sliding away at a…

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Q: Solve the differential equation y" - 2y + y using the method of variation of parameters. ਜ

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Q: Find the critical points of the function f(x) = x³ + 1¹5 x² + 50x + 8. Use the First Derivative Test…

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Q: Find the area of the region bounded by the graph y = sin x, y = 0, x = 0 and x =3π/2

A: Area of a region when strip taken parallel to y-axis is ∬dydx.

Q: 2x lim x-0 x²+5x

A: The given limit,      limx→02xx2+5x

Q: Q3/Evaluate four of the following integrais dx dx c. fd. sex C. sec²x e. f(3x + 2)5 dx

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Q: The average rate of change of f(x) = cos(x) with respect to x as a changes from 0 to π is 2 OOO 2 -2…

A: We have to find the average rate of change.

Q: 6 Consider the three by three system of linear equations 2x + Y + + 2y + 2z 5z 12. We will solve…

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Q: If you evaluate the integral expression |2x-1|dx the result is Blank 1 (use fraction or decimal in 2…

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Q: b.) Inside r= 3 sin and outside r= 1 + sin &

A: This is a problem related to area calculation of the polar curve. Based on the general formula and…

Q: Suppose f'(x) = 12√/1+4x where f(0) = 5. 1) Find the general antiderivative, f (x). 2) Use the…

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Q: S 10dz 4z³-4z² + 5z

A: We have to find value of given Integral using partial fraction.

Q: A rotating light is located 11 feet from a wall. The light completes one rotation every 5 seconds.…

A: This question can be solved using the rate of change of physical quantities.

Q: 3 п 2 2 cos² 4x dx

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Q: 6. a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0≤x≤ 2π 3 b) Classify each…

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Q: dx ylnx dy || y + 1 X 2

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Q: Determine the intervals on which the given function is concave up or concave down and find the…

A: The graph of  y =f(x) is concave up on those interval where f"(x)>0 . The graph of  y =f(x) is…

Q: Solve: 123 1 224 + 1 315 - 4x6 +...? +

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Q: 2. √√√x + y + xy = 21

A: We have to find out derivative

Q: A sort of "decay" Suppose that newly-baked cupcakes are taken out of the oven which is set at 100…

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Q: Compute the divergence and curl of F= -(z³-3x)j+4y²k+x²yi

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Q: x + y + z = 1 2 + 2 + 2 = 2 3 + 13 + 23 = 3 = 7 5 + + 5 + 2 9 = ? =

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Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: (a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of…

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Q: For the function, find the points on the graph at which the tangent line is horizontal. If none…

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Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x² + xy + y² - 9x…

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Q: S -1 etan 1+4t² 2t - dt

A: Let u=tan-1(2t)⇒dudt=21+(2t)2=21+4t2⇒du2=dt1+4t2 ∫etan-12t1+4t2dt=∫eudu2…

Q: 2.f(x) = = x3 3. f(x) = x tan x 4.f(x) = +₁₁ 4* x-1 1 x7

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Q: y" + y = 3x sin x

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Q: S x-6 x²+9 dx

A: To evaluate the given integral. ∫x-6x2+9 dx

Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx 7. p² sin 0 d0 dp Ꮎ dᎾ π/3 π/6 8. (2-y)dy dx 9.…

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Q: lim X- 12x²-x-1 1 8x²+2x 4

A: The given limit,         limx→-1412x2-x-18x2+2x

Q: 3. Let there be some a, b ER such that f(a)f'(a) = f(b) f'(b) + 1. Show that f f(x)f"(x)dx ≤ 1.

A: This is a problem related to integration. Based on the general formula and concept we will prove the…

Q: explain using a graph of (x) = X³-6x, for 0≤x≤3 With Six sub intervals, what the Riemann sum…

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Q: 7) Find the critical point (s) of f(x, y) = 2x³ + 3y² - 9x² - 30y + 12x-3. Then use the second…

A: solution is given below...

Q: Question 1 A triangular trough is 10 ft long, 6 ft across the top, and 3 ft deep. If water flows in…

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Q: Consider the R 2 − R function defined by f(x, y) = 3x + 2y. Prove from first principles that lim…

A: Let's evaluate given R2-R functions limit.

Q: given value of x. Show your complete solution.

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Q: 1. Use the Chain Rule to find 1. y = u² + 1 dy dx (show your complete solution) . u = x² - 1

A: dydx=4x3-4x