Find the particular solution that satisfies the differential equation and the initial condition. f'(x) = 4x, f(0) = 1 f(x)

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Q: 18. 2ху' + у %3D 6х, х> 0, у(4) 3 20

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Q: Evaluate the following a. 2/(1 + j4)

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Q: Find the centroid of the region bounded by the curves: y = 2x – x² and y = x

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Q: use mathematical induction to prove the formula for all integers n ≥ 1. 1+2+2^2+2^3+•••+2^n-1 = 2^n ...

A: Given the statement is "For all integers n≥1,  1+2+22+23+ ⋯ +2n-1 = 2n-1".

Q: Find the absolute extrema of the function on the closed interval. F(x) = x³ -?, (-1, 4] 2

A: Given,            fx=x3-32x2 , -1,4To find : Find the absolute extrema of the function on the closed...

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Q: The graph of the following function has two slant asymptotes. y = V 25 + 16x2 Find the equation of e...

A: NOTE: Refresh your page if you can't see any equations. . now asymptote is in the form of 

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Q: Determine the resulting surface area when the curve y = x is rotated about the y-axis in the interva...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: Find the area of the region bounded by the graphs of the equations: f (x) = V5x – 10 g(x) = 2x – 4

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Q: What is the chromatic number of the planar graph representing this map? A B G D E F K J M

A: now In this given graph the maximum vertex part of graph is either F or I (with 7 vertices each) Now...

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the giv...

Q: 5. Find the volume of the solid obtained by rotating the region bounded by y = x³,y = 0, x = 1 about...

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Q: 93x88

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: The system can be rewritten as the matrix equation 4 6. - 3 y Find the General Solution of the Syste...

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Q: Analyze and sketch a graph of the function. Find any Intercepts, relative extrema, points of Inflect...

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Q: Evaluate tot? xe*< + y2 + 22 dv, where E is the portion of the unit ball x2 + y² + z2 s 1 that lies ...

A: Triple integral 

Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 3 and...

A: Given query is to find the formula for polynomial p(x).

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Q: Solve the initial-value problem

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Q: Find the indefinite integral and check the result by 3/2 + 4x + 6) dx

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Q: Read Theorem 6.2 in the textbooke. Suppose that E cn an is a power series with interval of convergen...

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Q: y = 3x?+1 ; (0,1)

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

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Q: Q3)B/ Find the slope of the tangent line to the graph of x² cos(y) = 2y- eš* at the point (1? %3D 00...

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Q: A model for the velocity v of a skydiver is 4 = 9 – v². Then the value lim v(t) is__ 1 Enter the cor...

A: The given differential equation can be solved by using the variable separable method.

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Q: ple plot A modern window has the shape of a rectangle topped by an equilateral triangle as shown in ...

A: For the solution follow the next steps.

Q: If a(1) = 2, and a(k) = 5a(k-1) for all integers k >= 2, then what is the 4th term of the sequence? ...

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Q: Evaluate the integral. 7/6 (7/2 (5 p2 sin() dp de do Jo

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Q: A poster must have a printed area of 280 square inches. The top and bottom margins are 6 inches each...

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Q: Determine the derivative of the function f = log, | tan 5m + sec 5m| with respect to m. O cot (5m) r...

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Q: Find the area of the triangle with vertices P(1,6, –6), Q(0,0,0) and R(3, 4, 1). NOTE: Enter the exa...

A: Finding the Area by taking the vectors

Q: equation by integration x? dy + 3xy=x %3D

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Q: Being u, w positive values. Based on the information in the figure, select the couple that denotes, ...

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Q: Find the area of the triangle with vertices P(1, 6, –6), Q(0,0,0) and R(3, 4, 1). NOTE: Enter the ex...

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Q: Determine the length of the arc on a circle a? + y? = 100 from a = 3 to x = 5 in the quadrant IV. O ...

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Q: sinh(3r) 3. Solve for f(21) (x) given that f(x) = 3 %3D

A: We know, ddxcosh(mx)=msinh(mx) , for any real number m. ddxsinh(nx)=nsinh(nx) , for any real number...

Q: Let f(x)= (2x-3)/(x-3). Find the interval(s) where f(x) is concave up, and the interval(s) where f(x...

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Q: Solve (cosxcosy-cotx)dx-sinxsin?ydy=D0. O sinxcosy=In(ccosx) sinxcosy=-In(ccosx) sinxcosy=In(csinx) ...

A: Let's find. 

Q: Approximate the critical numbers of the function shown in the graph. Determine whether the function ...

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Q: sec* (2t) dt tan° (2t) cot (2t) cot (2t) + c cot*(2t) cot°(2t) + c C. 12 16 12 16 1 16 tan (2t) + c ...

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Q: Use the Lagrange multipliers method to find the maximum and minimum values of the function f(x, y) =...

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