Use separation of variables to solve the differential equation explicitly for u. du dt = 4 + 4u + t + tu

Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

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Q: Find the average rate of change of the function f(x)=8-3x between x = -4 and x = 1. Type an exact…

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Q: Find the total area of the shaded region. Ay 2 y = 3 y = 3 sin ² x X The total area of the shaded…

A: The area between the curves y=3sin2x and y=3 on interval π2, 3π2

Q: ← Write the expression as an algebraic expression in u, u > 0). cos sin cos sin 1 1 2 2 = (Simplify…

A: We will find the solution

Q: Prove: sec 0 + tan(-0) cot 0 - cos (0) = sec 0 tan 0

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Q: Find the area of the "triangular" region in the first quadrant, bounded on the left by the y-axis…

A: Solution is given below:

Q: 9).  Find the general solution to the differential equation. y' = 2xy2 y =     PLEASE SHOW STEP BY…

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Q: Find the solution to y' =    2y satisfying y(0) = 15

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Q: 1. Find the Laplace Transformation of the following function. First express the function in terms of…

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Q: Find the indefinite integral. (Use C for the constant of integration. Remember to use absolute…

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Q: Work Problem 3. a) Find the local maximum and minimum value(s) (if it exists) of the function f(x,…

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Q: Determine the equation of the parabola whose graph is given below. Write your answer in General…

A: We have to find equation of parabola which is given in the graph. We know the equation of parabola…

Q: 23) . Find the solution to the differential equation y' =    5y satisfying y(0) = 18.   y(t) =

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Q: Using the Mean Value Theorem, how small can ƒ(21) be, given the conditions below? f(3) = 17 and…

A: The objective of the question is evaluate the smaller value for f(21 )with help of given condition.

Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

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Q: d the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 6x²+x-1 8x2 - 6x - 5…

A: Topic:- limits

Q: Consider the parametric curve given by (a) Find dy/dx and d²y/dx² in terms of t. dy/dx = |d²y/dx² =…

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Q: Find the limit of the transcendental function. (If an answer does not exist, enter DNE.) cos(20)…

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Q: Use implicit differentiation in finding y'. 1. x²³+y³ =18xy 2. x²y+xy² = 6

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Q: Find the domain of function = 2x² 2 e f(x 0

A: We need to find domain.

Q: expand e^2x in powers of (x-1)

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Q: How many critical points the following function has, f(x, y) = x³ + x + xy² - 5? Select one: 0 1 0 3…

A: The objective of the question is determine the critical points of the given function and choose the…

Q: Find the absolute extrema of the function. et². 9 - h(x) = on [-3, 3] Absolute maximum value: (No…

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Q: t Find the Taylor series centered at c = -1. 7 3x-2 f(x) = Identify the correct expansion. Σ -(x -…

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Q: Solve this distance, rate, time application involving a rational equation: It takes the same amount…

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Q: K Find f(x) dx for each graph of y=f(x), where f(x) consists of line segments and circular arcs. 0…

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Q: The estimated marginal profit associated with producing x widgets is given by P'(x) = -0.6x + 24…

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

Q: Rewrite the equation with the variables separated. dy dx + √y = e* √√y dy √y-1 dy dy = ex dx = (ex -…

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Q: Let y = 2(x - 5)²-6. Part A: Is the given relation a function? Is it one-to-one? Explain completely.…

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Q: A radioactive isotope has a half life of 1 min. The amount of material, A(t), at t = 0 is 10 kg.…

A: A radioactive isotopte has a half life of 1 min. The amount of meterial, At, at t=0 to 10 kg.To…

Q: Find the general solution of the differential equation. y(4) +12y" + 36y = 0. NOTE: Use C₁, C2, C3,…

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Q: Integrate the given series expansion of f term-by-term from zero to x to obtain the corresponding…

A: We will solve to get required result.

Q: Find a formula involving integrals for a particular solution of the differential equation y" - 15y"…

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

Q: A company's marginal cost function is MC = 28x4/3 - 14x3/4 + 1, where x is the number of units, and…

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Q: Find the limit (If it exists). (If an answer does not exist, enter DNE.) Im 2 X-3+x+3

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Q: 11) Find the general solution to the differential equation. y' = eyx2

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Q: anufacture the OP(s) = -5²+105s-1,000 OP(s) = -s²+55s- 1,000 OP(s) = -s²+105s + 1,000 OP(s) = -5²…

A: topic:- calculus

Q: A. Find the roots of the following differential equations and match with their complete solution.…

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Q: Consider an object moving along a line with the given velocity v. Assume t is time measured in…

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Q: Use the binomial series to expand Select the correct answer. O1+1.3.5 n = 1 0₁ + $ 1 n = 1 (-1)…

A: Given the expression is 11+x2 Note:     Multiple questions are given, we are answer only one…

Q: A Sliding Ladder A 26 ft ladder leaning against a wall begins to slide. How fast is the top of the…

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Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: To find the antiderivative F of f that satisfies the given condition. To check the answer by…

Q: Use the definition Prove that: d dz sin z = cos z The low f(z) = lim Δz→0 f(z+Az)-f(z) Az

A: Topic = Derivative

Q: Evaluate the integral using an appropriate method. T/3 x sin(3x) dx

A: ∫0π3x sin(x)dx

Q: 9. Find the solution to satisfying y = dy dt = 7y || y(6)=9

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Q: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the…

A: The given sequence an=6n+7n1n

Q: The graph of the function f is shown below. If m is the slope of the line tangent to the graph of…

A: From the given graph, we have to find the slope of the tangent line at x=-7

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: We need to find domain.

Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) lim Write a…

A: topic - limits