7. Inx dx

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

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Q: b/ Find the solution to the homogeneous differential equation below dy x²+y² dx 2ху

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Q: nd the area of the region under the graph of f(r) = 2r² – 4x + 2 on [-2, 3].

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Q: The values of C, and C2 so that y(x) = C, sin x + C, cos x satisfies the following conditions: y(0)…

A: Substitute x=0 in y(x)

Q: The function f is shown below. What is the value of f(x) dx? Write your answer in simplest -5 form.…

A: The detailed solution is mentioned in the step 2

Q: Find Duf at P. 2. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i+ 1 Duf = i

A: We need to find directional derivative at p.

Q: The Tojolobal Mayan Indian community in Southern Mexico has available a fixed amount of land.1 The…

A: As per our guideline we are supposed to be answer only first three subpart of the question you can…

Q: 6) Answer the following True or False: Let  f(x) be a differentiable function, such that f(1)=−9…

A: The solution is given in the next step.

Q: What is the a value of x such that sinx = .? 3 = 24.5° = 53.6° = 41.8° = 38.7°

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Q: Identify the range of arctan(x) so that the relation is a function. O-<y< ! - I <y< I 0<y< 7I

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-8, 5,…

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Q: Find sin( ). (Hint: Use the half-angle formula.) arccos 3/10 V10/10 3V10/10

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Q: 4х if х> -1 f(x) 3D { 5 — х2 if b < x<-1 Зх + 7 if x < b

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Q: Given f(x) = 1 –(5+ 10x) + (5 + 10x)² – 27 (5 + 10x)³ then f'(x) =, %3D - (5 + 10z) – ( 5 +…

A: f(x)=1-32(5+10x)+94(5+10x)2-278(5+10x)3 Then f'(x)=0-(32×10)+(94×2×5+10x×10)-(278×3×(5+10x)2×10)…

Q: 10. Find the first partial derivatives of the following functions (it is not necessary to simplify).…

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Q: Find the volume of a right pyramid that has a square base in the xy-plane. – 1 < a <1, -1 < y < 1,…

A: Given right pyramid with square base. Side length(a)= 2 units Height(h)= 3 units

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A: Given query is to find the the population and rate of change of population after 20 years.

Q: 9. cos(x-)

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Q: 6. Find the area of the region enclosed by the graphs of y = VT+1 and y = r – 2 and the vertical…

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Q: x = In(1– y²) 0<y <½ for Determine the arc length of the curve

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Q: Зх — у 3 4 -2x +y = 5 - %3D

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Q: 2-9 dv

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Q: Find the derivative of the following using First Principle. 1) y = 1 2) у %3D х 3) f(x) = 5x3 %3D 4)…

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Q: Given that Vf (7, -9) = 11 i – 6j, find the directional derivative of the function f at the point…

A: Given,           ∇f7,-9=11i-6j.            The function f at the point 7,-9 in the direction of…

Q: Evaluate/Find the following integrals. 2 1. SxV4x – x¯dx

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Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 The areas…

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Q: Find sin({ arccos ). (Hint: Use the half-angle formula.) 3/10 V10/10 3v10/10

A: Find the following

Q: e^x + y)dx +(2 + X + ye^y)dy= 0 ,y(0)=1

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Q: Choose the graph of the function arcsec(x).

A: Given that fx=sec-1 xTo draw: the graph of fxSolution :

Q: Find the directional derivative of f(x, y, z) : 4y at P(3,1, –2) x + z in the direction from P to…

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Q: Consider the following. -2 ifx -1 if x = -1 fix) = -2 y -2 -1 <-1 -3 Use the graph to find the limit…

A: We need to find limit at x→-1.

Q: Block A is sliding across a horizontal and frictionless surface when it collides with block B as…

A: We have to find the initial speed of block A.

Q: (7/6 sin t dt cost 39.

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Q: 3 +e? +). 3x 2x2 2

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Q: A closed rectangular box with a volume of 375ft° is made from two kinds of materials. The top and…

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Q: find the LaPlace Transform, L{f(t)}, the given f (t). f(t) = e 3t sin 2t 2 s+ 3 2 А. (s + 3)2+ 2 (s…

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Q: Evaluate the integral of· if it has an upper limit of 1 and a lower limit of 0. (x+1)®

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Q: Find the area of the region bounded by the line y = 4 - 2x and the coordinate axes. Draw the graph

A: Given query is to find the area bounded by the line.

Q: Q11. Obtain the general equation of the curve whose slope at any point is equal to y - 2x.

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Q: 3x + 2 dx Vx + 1

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Q: Find the first, second and third derivatives of the following total cost function w.r.t. Q: TC =…

A: Differentiate with respect to Q.

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-8, 0,…

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Q: Solve the system of linear equations 3x-y+2z=-21 4x-2y+z=-31 -x+3y-2=11

A: We have to solve the system of linear equations.

Q: 33. (1 + r)' dr

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Q: (2²ª + 2w)* 3 Find dy/dx, given the following: y = V2x–4 (23+2x)"| V(22–4) 17 –360² +102 –24 (2x–4)ª…

A: Given: y=x3+2x32x-4   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The…

Q: Your explanation should answer WHY you are doing the work and HOW you are doing the work briefly…

A: If f'x is:→ then fx is-ve→decreasing0→horizontal +ve→increasing=a &amp; ≠0 →slant with slope…

Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: Given the function graphed below, evaluate the definite integrals. 3. 2. 4 -2- -3 -4+ f(z)dz =…

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Q: 4. [Geogebra Question] Let f(x) = (1 – x) In(x²)+3.0225887223. Use Geogebra to find the definite…

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Q: Q3. Evaluate the integrals below. For each integral, first calculate the related indefinite inte-…

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