Solve: dy = (x – 3y) dx %3D xt = (3t2 + c)e2t b. 9y = 3x – 1+ ce-3x %3D -3ex + x3y C = 0 +e + a.

Q: The graphs of f(x) = x² - 4 and g(x) = x2 - 4 are shown. y 8 8 6 fx) = x -4 6 g(x) = x -4| 4 2 2 -2 ...

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Q: b. Homogeneous Coefficients y(x2 + y?)dx + x(3x2 - 5y2) dy = 0; when x = 2, y = 1

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Q: Solve these differential equations G. s(1+√(t ))dt+t√(t ) ds=0;when t=1,s=1 H. (y^2-xy)dx+(x^2-xy)dy...

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Q: (a) Let 7 : [a, b]→ R" be a curve with 7 (t) + 0 for all t e that the reparametrization by arc-lengt...

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Q: (D² + 49)²y = 0 (D² + 36)²y = 0

A: We have to find the general solutions of D2 + 492y = 0 D2 + 362y = 0

Q: 00 S xe хе ¯*¨dx

A: The given definite integral is: I=∫0∞xe-x2dx Substitute -x2=t⇒-2xdx=dtxdx=-12dt Also when x→0, t→0An...

Q: 4. y" + y = tan x.

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Q: n2 of 6 Calculate the difference quotient for f(x) = x + x at a = 9. (Express numbers in exact form....

A: topic - equation of tangent to the graph

Q: Find the area bounded by the curve ay = x² and the lines y = a and y = 4a. %3D

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Q: 9. For the function whose graph is drawn below, identify the x-values in the open interval (-4,7) wh...

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Th...

A: This question is based on Rolle's theorem.

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend 6...

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Q: d. Bernoulli's equation y' +y = e*y+ 1. 2. xdy + ydx = xy?dx

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Q: = Evaluate : x V1+x² X' dx 1-х?

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Q: (b) Let C denote the boundary of the quadrilateral with vertices (1,1), (1, 2), (2, 1), and (2,3), t...

A: Given F→=(ex4+y2,xy+sinlnx

Q: Which of the following is a polynomial function that might have the given graph? O A. f(x) = 2x(x+ 3...

A: FOR THE GIVEN GRAPH

Q: 12) L10 -10 -5 5 10 10 12 10 L10 Y10 -5 -5 10 10 Label any intercepts. (If an answer does not exist,...

A: Find x, y and z intercept. 

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that: ddxsechx=-sech...

Q: 3 3 sin(x²) dx dy y by reversing the order of integration. With order reversed, I sin(x?) dy dx, whe...

A: Given:  Let I=∫03∫y3sinx2 dx dy To Find:  To evaluate the given integral by reversing the order of i...

Q: lim f (x), uate left hand and right hand limits.) Here, |x lis the gr

A: Given that: f(x)=x1x ,    -3≤x≤3

Q: [4] Solve for x in the equation: arctan(x+1)+arctan(x-1)=arctan(12)

A: Topic = inverse Trigonometric ratios  solution of eqution x=43

Q: Consider the solid that lies above the square (in the xy-plane)R=[0,2]×[0,2], and below the elliptic...

A: Here is the solution of the given problem.

Q: Find the total force of water pressure exerted on the glass window of an aquarium with the following...

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Q: Consider the following. w = xyz, x = s + 3t, y = s - 3t, z = st? (a) Find ôw/as and aw/at by using t...

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Q: 2 4 (6x2 + y ) dx dy =

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Q: C. Evaluate the definite integrals ( show your solutions) 1. S, (x³ – 6x² + 2x)dx - TT 2. 3 cos3 3xs...

A: The given questions can be done as follow:

Q: Consider the function f(x) = x7 + 1 Use the Intermediate Value Theorem, if applicable, to determine ...

A: This question is based on Intermediate value theorem.

Q: (a) Show that the vector field F(x, y, z) = (x² + y², æ, z*) is not conservative.

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Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the tri...

A: Given that: Altitude of a triangle is increasing at a rate of 3cm/minArea is increasing at 4.5 cm2/m...

Q: 11. (D² – 2D + 5)y = 0 12. (D² + 9)y = 0

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Q: 2. Evaluate the following integrals. a) [ex.sech (e2x + 1) dx b) [sech (2x-1) dx c) Vsinh 2x cosh(2x...

A: Integration by substitutions

Q: 3 dx x² -1

A: Let I= Integration of x3/(x2-1)1/3  ------(1)

Q: dy CSC X Find for y 3= dx 1+cSC X dy dx

A: We have to solve

Q: Determine the particular solution of the given differential equation. y(x? + y?) dx + x(3.x² - 5y²) ...

A: Given equation is Homogeneous Differential equation.

Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx s2n? ...

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Q: 4. Let b > a > 0. Show that (a,b] is neither closed nor open.

A: Explanation of the solution is given below....

Q: Solve the following deferential equations using variation of paramet 2. y"-2y'+y=

A: Topic = Differential equation  As per guidelines,  At a time only one question can be answered out o...

Q: Calculate the derivative. f(x) = (4e* – 5x²) (x³ + 1) - (Use symbolic notation and fractions where n...

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Q: Find an equation of the tangent line to the graph of the function at the given point. 3x + 5 f(x) (2...

A: topic - equation of tangent line

Q: 4. y" + y = tan X.

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Q: Let R be the region bounded by the curvesy² = 2 - x and I = y. Using rectangular strips parallel to ...

A: Given that:                                  

Q: Vhich of the following is correct about the statement: "A separable DE is also an exact lifferential...

A: We have to find

Q: 4) Find the third derivative of g(x) = e*.

A: We will solve the problem 

Q: Consider the effect of gravity on falling objects. If you drop an object, from rest, on earth, it wi...

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Q: The table below gives values of f(x) = ex For the data, evaluate f ' (1.0) and f '’(1.0) with the f...

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Q: Calculate the derivative. f(x) = 9 – 15x1/3 + 4e* %3D (Use symbolic notation and fractions where nee...

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Q: [e2= + 2**]dx

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Q: Suppose log,(r) = 4 and log,(y) Use properties of logarithms to evaluate the following. (a) log, (b)...

A: As we know that the logarithmic properties: i).logbmp=plogbmii).logbm·n=logbm+logbniii).logbmn=logbm...

Q: Find the limit. 1 lim COS x-4 4

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Q: (a) Let f : Z+ → R, and g : Z, → R. be functions. We say that f e O(g) (“f is big-O of g", usually d...

A: a.f:ℤ+→ℝ+ and g:ℤ+→ℝ+We say f∈O(g) if there exist a constant c∈ℝ+ and n∈ℝ+ such thatf(n)≤c·g(n) for ...