Solve the initial-value problem. x(t) = x" + 3x' + 2x = 1 + t², x(0) = 0, x'(0) = 2

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Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: finding Ⓡ a se lim, soo Jn. = JA n

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A: Given differential equation is:

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A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

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Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

A: Dear learner, As per our guidelines, we can provide the solution for first three parts only. Kindly…

Q: Assume that the random variable X is normally distributed, with mean μ = 70 and standard deviation…

A: To find the probablity P(X>a)  then we have to convert the expression into  Z-score value of the…

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Q: and b given that 3 f(x) dx - [² 5 = 5 and b = 1 = 1 and b = 5 = 0 and b = 5 - = 2 and b = 6 1 f(x)da…

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Q: 10. Find r(t) if = (4t3+ 4t)i + 6tj + 3t²k, r(0) =i+j.

A: We have to find out r

Q: 11. Draw a high-quality graph by hand on graph paper for the function f(x) = 2x³ + 6x². Your work…

A: Given :  f ( x ) = 2x 3 + 6x2  find minimums , maximums and inflection points ,  And intercepts

Q: Solve the system of equations by any method. -3x+6y= 27 x - 2y = -9 Enter the exact answer as an…

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Q: A region bounded by f(x) = 5 — x, y = 0, and x = 1 is shown below. Find the volume of the solid…

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Q: Assume that f is continuous on the set of real numbers. Find a and b given that cb 3 f(a)da - [³…

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Q: where a = and b = 16 10% f(x) dx = f* f(x) 10 24 [*1 (2) dz - f(2) f(x) dx

A: To find the value of a and b.

Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

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Q: 6. Find the radius of convergence and the interval of convergence for Σ-0¹ (x - 2)". 7. Find the…

A: See this solution in below.

Q: Consider the integral 11 [™ (22² + 2x + 1) da (a) Find the Riemann sum for this integral using right…

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Q: Find the coordinates of a point on the parabola y=−x² where the slope of the tangent is 5. x+3x+4

A: The given parabola is y=-x2+3x+4 We need to find the coordinates of the point on this parabola where…

Q: Write an equation for the function graphed below. The y intercept is at (0,-0.3) 5 4 3 2 1 + -6 -5…

A: We have to write an equation of given graph.

Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: ( (tano-1)² do

A: Given ∫[tanθ-1]2 dθTo evaluate the integral:

Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x)…

A: To find the following values.

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

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Q: Find the largest product the positive numbers x, y, and z can have if x² + y + z = 4. The product is…

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Q: 8. 9. A) 1−sinx Ĵ (COSX + 1 COS X+X 2(cosx+x)2 E) ·x)³ dx = ? 1+tan²a (2 + tana)² -+C B) +C D)…

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Q: Use the properties of the derivative to find r(t) = 3/i+6f³j+31³k u(t)=2i+2r²j-3t³k [r(t) - u(t)]…

A: This question is related to derivative, we will solve it using given information.

Q: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

A: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

Q: Q5A) Find volume of body from above Z=√4-x² - y² and below Z Triple integration. 1 using

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Q: Law of Sines Law of Cosines Maze Round all angles to the nearest degree and all sides to the tenths…

A: Disclaimer : Since you have posted a question with multiple sub-parts ,we will solve first three sub…

Q: Solve the differential equation: dx dy + x = e-y.sec²y

A: Here we have to solve the differential equation.

Q: Find the directional derivative of f(x, y) = x² - 2xy at the point (1, -2) in the direction from…

A: directional derivatives

Q: a. Find a curve with a positive derivative through the point (1, 1) whose length integral (Equation…

A: To find curve satisfying the given conditions.

Q: B)Prove (cose + i sine)" = cosne + i sin ne

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Q: +√³1 (2) dx = -3 and ³ S If it is known that [²₁ √f (a) da = 4, find the value of f(x) dx.

A: To find out the integral value.

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4…

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Q: Ju 2²u Consider the heat equation = Ət for a bar of length L=1, with non homogeneous boundary…

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Q: (C) For what values of x does the series 11=1 (D) Find Taylor series at x=2 for the function ala…

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Q: 2 2(x + 1).In(x ² + 2x + 3) x²+2x+3 $² A) In(x²+2x+3) + c dx = ? B) In²(x²+2x+3) 2 +C

A: According to question,Given Integral,Let I =∫2x+1 lnx2 + 2x + 3x2 + 2x + 3 dx

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Q: If f is the function given by ƒ(x) = √²* √t² — t dt, then ƒ' (2) = 7 a. 2√12 b. √2 c. √12 d. 2√12 B…

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Q: Since the creation of a social program, the percent of persons 65 years and over with a family…

A: Here we have to us ethe given function.

Q: dy B)Solve differential equation dx -(x²+y) x+siny

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Q: Stan 2xdx O-In(cos 2x) + C O-In (cos 2x) + C O-In (sin 2x) + C O tan² 2x 2 + C

A: INTEGRATION

Q: let a a E R - {0} and g the function defined by : sen (2) si z #0 az g(x) = 5 si z = 0 The function…

A: In this question, we want to know for what value of a , the given function g will be continuous on…