. Solve the following problem (a) Y'(t) = XY(t) + 1, (b) Y'(t) = \Y(t)+t, Y(0) = 1. Y(0) = 3.

Q: 4.) Give the general solution of the following ODE: x" + 3x - 4x = 0.

A:

Q: ૩ 3* sech³ (3) 1+tanh (3) S- -dx

A: Substitution method in integration: To simplify the integral, in the given integral independent…

Q: 4. Swin (w - 2) dw

A: The given integral is: I=∫wlnw-2dw   Apply the integration by parts to solve the above integral.…

Q: Let f(x) = e2sinx 1. Use the local linear approximation of fat x = 0 to approximate e2sin (0.01)

A:

Q: Find the grea i) Sketch the ii) Determine the iii) vet up iv) Integrate 7) y=vin of the boundaries a…

A:

Q: / (csc 2x)(cot 2x cos 2x + cot 2x cos 2x) dx

A:

Q: Find the point on the line y = 4x closest to the point (1,0). (Use symbolic notation and fractions…

A:

Q: cos³ 3x sin 3x dx

A:

Q: * (sin(2a) + cos(2x)) da Jo

A:

Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: 6. How many outfit combinations can be put together from 6 shirts, 3 pairs of pants, and 4 pairs of…

A: Total shirt = 6 Total pants = 3  Total shoes =4

Q: 6. S t √1+2t dt

A: The given integral,    ∫t1+2t4dt

Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: We will first sketch the curve and the line.

Q: Perform the integration. 3 ² (13* - 11 + 13x − 31) dx - 0

A:

Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

A:

Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? O 0 02 Ο ΝΑ x-coordinate of the…

A: Solution is given below:

Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: y-coordinate of the centroid of the plane region bounded by 17 What is the the x-axis and the…

A:

Q: 1. Find the area of the region bounded by the curves y = 3x and y=x².

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Evaluate the following: 4 fsin 2xcos²2xdx

A:

Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A:

Q: 1. Use local linear approximation to estimate In (0.99). 2. Find the absolute extremum values of…

A:

Q: y-coordinate of the centroid of the plane region bounde 22 What is the y = 2x + 1, x + y = 7, and x…

A:

Q: lim (tan x)(sin x−1) + TU x-2

A: lim     (tanx)(sinx -1) x -->π/2 here we can direct put limit  because we can apply limit

Q: Evaluate the limit: lim (x - Inx)* x→0+

A: Using limit definition

Q: -0.03t The function f(t) = 9000 e represents the rate of flow of money in dollars per year. Assume a…

A: Given that,

Q: P 1. (1 Use the cylindrical shell method to find the volume of the solid obtained by rotating the…

A:

Q: 11 12 13 14 15 Solve Solve Solve Solve Solve ((AND)U(CNA))-(CNB) (BUC)-(DNA) (BUD)-(ANC) (ANB)U(DNC)…

A:

Q: Find the area bounded by y = 2 - x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE A D E

A:

Q: 10. The sale price of a book after a 25% discount is $40. What was its original price? $46.67 O…

A:

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

A:

Q: Set up the double integral that will find the volume of a solid bounded by z = 1- y²x² and the xy-…

A:

Q: Solve

A:

Q: (sinhz)(coth’z+csch*r)dz

A: Integration is done.

Q: Evaluate the following definite integrals using the Fundamental Theorem of Calculus:

A: The given two integrals are:a∫-552xx2+2dxb∫01x3+1x+1dxFundamental Theorem of Calculus says:If Fx is…

Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

A:

Q: 9. A child is flying a kite with a 45-ft string at an angle of elevation of 50°. Which of the…

A: Let's find altitude of the kite in feet.

Q: | (sinh x)(coth’x + csch3x)

A: The solution is given in the next step.

Q: 3 2 พ 2 cos2 4x dx

A:

Q: What is the integral of (2 sec^2x - sinx) dx? * O 2 cosx+tanx + C 2 tanx + sinx + C 2 tanx + cosx+C…

A:

Q: lim (sech 2x) csch x² +0x f(x) = csch x

A:

Q: Find the area bounded by y = 2 - x² and y=x a. 9/2 b. 7/2 C. 5/2 d. 3/2 e. NONE OF THE ABOVE

A:

Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A:

Q: The following differential equation is a Bernoulli equation: 2 dy + y3 where y = f(t) dt t By making…

A: Using substitution Z=y^n, and n=1/3 We get the linear differential equation

Q: -.f x³ ex² dx 3

A:

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: derivative

Q: Q3. Evaluate : IL (2) * dy dx

A:

Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative