1. Evaluate the improper integral 150 xe dx or state that it diverges.

Q: Find r(t) if r'(t) = 4t³ i + 5t+j + √tk and r(1) = i + j. r(t)

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Q: 4) If y = 2√x - 2 tan-¹ √x, then y 1 -1 1+x²*

A: We have to find y' for the given function.

Q: 63 x dx 3√ √x²+1 S √(x² + 1)² + C Option 1 O (x² + 1)² + C Option 3 213 √(x² + 1)² + C Option 2…

A: We have to evaluate ∫x dxx2+13.

Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-z = -2

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Q: The figure to the right shows the velocity, v (in feet/second), of a runner for 0 < t < 15 seconds…

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Q: A company can produce LCD digital alarm clocks at a cost of $6 each while fixed costs are $50.…

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Q: 3 -21 3 -1 The Cofactor Matrix is :- -3 0 [-3 0 12] 606 6] 36 ن من من IF A [-3 0 12] 606 3-6 6…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: The volume of a solid E is given by 9-1² 9-x²-y² 1.***** 1 dz dy dx -3 JO 0 (a) Sketch each of the…

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Q: Find the indicated limit if it exists. √x+4-2 a) lim X-0 X 8x³+27 b) lim x-1.5 2x + 3

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: I am attaching image so that you understand each and every step.

Q: 2) Find the oneer bounded by x = 3y²-9, x = 0, y = 0, y = 1 a) 8 b) 6 c) 4 d) wone of the above

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Q: f Cos 6 x dx 2 Cos ²3x

A: Solving the problem by finding the value of the problem.

Q: 55,000 Suppose that the demand function for a product is given by D(p) = and that the price p is a…

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: We can solve the differential equation.

Q: Find the equation of the line L2, pass through the point (2,-1) that is parallel to the line L1…

A: The line L2 pass through the point 2,-1 that is parallel to the line L1: 2x+4y=12

Q: Q5) Find dw/dt at the given value foe the following functions 2) w = 2ve* - lnz.x = ln(t+1), v =…

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Q: Determine the intervals over which the function shown below is continuous. Enter your answer in…

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: A company discovers that to produce a = 890 new electronic parts, it will cost y = 980 new…

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Q: Let v(t) = (t², -4t,9). Compute the derivative of the following function. v(e¹)

A: Solve the following

Q: Consider the following autonomous first-order differential equation. d = y In(y + 2) Find the…

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Q: Find the derivative of the function. f(s) = √5-1 √5 +3 Choose the correct answer below. 2 O A. √5…

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Q: Laplas Inv Q1/ Find -1 s² (s+1)(S-1)²

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Q: Consider the following function, f(t) A. All reals. B. All reals except t = 1 and t = -1 C. All…

A: f(t) = t/(1-t)2 domain means input value which we can input in function and function is valid f'(t)…

Q: QUESTION 1 Check all statements that are true. If p is a polynomial of degree n, and q is a…

A: Note:- As per your mentioned staement no. I am solving only statement 4th here.

Q: Q2: Find y(2) if D.E as give 2 dy+3y=sin 2x, y(0) = 6 dx Given

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Q: Calculate the work (in joules) required to pump all liquid out of a full tank. Assume a = 6 m, b =…

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Q: A particle start from the point (4,4) and it's coordinates change by the increment AY=5 and AX= -8…

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Q: Find the derivative of f(y) = 2 sin y + sin² y and then use it to find all coordinates on the graph…

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Q: If, in a monopoly market, the demand function for a product is p = 150 − 0.10x and the revenue…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Determine whether the differential equation (7x² - 2xy + 6) dx + (7y² − x² + 7) dy = 0 is exact. If…

A: The differential equation,    7x2-2xy+6dx+7y2-x2+7dy=0

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: The given differential equation,      2y'+y=7t2

Q: How many years are required for an investment to double in value if it is appreciating at the rate…

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Q: 10. Show that there is a root of cos(x): = in the interval (0,7). TT Do NOT find the root. Explain…

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Q: The exponential function given y H(t) = 80,031.49(1.0483)', where t is the number of years after…

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Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: 2 Heather has a bag of 15 red, 11 orange, 9 yellow, 12 green, 6 blue and 11 purple markers. How many…

A: Heather has a bag of 15 Red ,11 orange ,9 yellow ,12 green ,6 blue and 11 purple. Find how many time…

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: Q21 By using Adjoint method, find the inverse of the following matrix. [1 -3 -1 A= 4 2 LO 2 Add file…

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Q: 1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ H-3- I-3 f(x) = { 2 -x+4 x - 3 x <3 I 23

A: Topic = Limits As per guidelines , At a time only one question can be answered. please repost for…

Q: 11. A hockey player, on left defense, is about to take a shot on net. The net is 1.83m wide. The…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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Q: Use calculus to find the open intervals on which the function f(x) = x+8√√/2 − x is increasing or…

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Q: Use the graph and the function to find the following. a) Find lim k(x). X→-1 b) Find k(-1). c) Is k…

A: We need to check the continuity of the given function in the shown graph.

Q: 3 Q4) Suppose a class contains girls, and boys. Suppose that 40% of the girls have long hair, and…

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Q: Find an explicit solution of the given initial-value problem. +²dy x=y=xy, y(-1) = -4 dx y =

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Q: Determine the law limit applied in solving lim 3 = 3. t-1 A. Limit of an identity B. Limit of a root…

A: Solution ) limit of a constant  limx→a b = b  limit of x tending to any value is value of the…

Q: The triangle inequality is the most common algebraic tool for rigorously proving order…

A: Note:- As you want the answer of 4th statement so i am solving only it.