3. An equation of line tangent to a curve at the point (1,3) is y = 2 + x. If at any = 6x, find an equation of the curve that satisfies the given d²y dx² point (x, y) on the curve, conditions.

Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3. A (e²-1)² e2 sq. units (e³ + 1)² e3 (e²+ 1)² e²…

A: Given:-the region bounded byf(x)=ex, g(x)=e-xand x=3

Q: Find d2y/dx2 for y2 + 2y = 2x + 1

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

A: Let's find  initial population and after 10 year population.

Q: Solve the integral: S- ® in/1+x A) an 1 B_5n/1+x' 5 6 1 √√√x + x + C + C c dx

A:

Q: Solve the integral: Seln(2x²+3x-4)³ (4x+3)dx eln(2x²+3x-4)³ A (2x²+3x-4) (2x²+3x+4)*(4) 3 B + C…

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Q: Cx²e*dx

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Q: The improper integral A 1 B 0 C St edx is

A: To solve the improper integration.

Q: sinh x tex + ex cosh x In the indefinite Integral in(cosh x + ex)- sinh x tex A In(cosh x + e*)-…

A: Answer: A

Q: Find the area bounded by : f (x)=e*, g(x)=ex and x=3. (e²+ 1)² A sq. units e2 B (e³ + 1)² e3 sq.…

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Q: y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: y=Arccos (x²)

A: I am attaching image so that you understand each and every step.

Q: ? Question af Use Mathematica to find the other partial derivative for the function dx f(x, y) = x²…

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Q: Q3/ Find a volume for the region bounded 4/X and Y = (X-3)² about the x-axis.

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Q: Which of the following is NOT a method for finding volume of solids of revolution? A conic method B…

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Q: V = 8TT². Which is the correct expression for dV dr dh 16ПР- dt dt dV dr = 16Tr dt dt dV = dt dV dr…

A: Topic:- application of derivatives

Q: Suppose that f(x, y) = ²/" on the domain D = {(x, y) |0 ≤ y ≤ 1,0 ≤ x ≤y³}. D Then the double…

A: Given: fx,y=exy and D=x,y| 0≤y≤1, 0≤x≤y3   As we know the basic integration formula.…

Q: Transforming S Ⓒ √ 2²-22²2 =2 A -dz 1+z² z²+z B -dz 1- © S с © S D N dx using miscellaneous…

A:

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: dy Reduce the linear DE (2xy + x²+x¹) dx = (1+x²) dy=0 to standard form dx (A) +y dy dx -2x 1+x² =x²…

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Q: y= 3 Arcsec 3x

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x+1. 3 A unit² 3 Ⓒunt² unit² D…

A: topic- area bounded by curves

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A:

Q: Find the area bounded by : f(x)=e*, g(x) = e¯* and x=3. A (e²-1)² e2 sq. units B (e³-1)² e3 sq.…

A:

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A =C sin x sinx cosy…

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Q: 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: We have to solve

Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a right triangle with…

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Q: 1₁ (16-x²) dx -1 What is the approximate area of the given function using the Right Riemann Sum…

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Q: y = Arctan (2x)

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: At what points does the helix r(t) = (sin(t), cos(t), t) intersect the sphere x² + y² + z² = 82?…

A: This question can be solved by putting x=sint, y=cost, z=t in the equation of sphere to obtain the…

Q: Determine the integral: [x²cosxdx A x²sinx + 2xcosx+2sinx + C B x²sinx + 2xcosx-2sinx + C (C)…

A: Given,∫ x2cosxdx

Q: Vector-valued function R(t) = 1. Reparametrize R using the directed arc length s from the reference…

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Q: y'+xy=xy^3 Solve for the solution What is the integrating factor? What is the dependent variable?

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Q: A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.

Q: 4. When solving an auxiliary equation of a certain differential equation the roots m = 1 ± 2j are…

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Q: 25. (x + 2y)dx + (2x + y) = 0 A. Exact B. Not Exact 26. (2xy2-3x2)dx + (x² + 2y)dy = 0 A. Exact B.…

A: as per bartleby guidelines i can solve only first 3 questions, please ask other separately

Q: 2x-1 a. √ (2x + 1) e ¹-¹ dx

A: The given integral is ∫2x+1e2x-1 dx We solve the integral using integral by parts formula. From…

Q: Q/IF 3 = sin(x) 0²³²141 y= (4) y = 3/2 I sin(x) cos(x) Prove that

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Q: iven ·S. A (-∞0,00) B) {0,1} Ⓒ(1,00) D) (-∞,1] dx, determine all value/values of P for which the…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and 1 A -unit² 3 B -unit² 3 -unit² 4 1…

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Q: The function is X 2 = y² What is 8²% მ2 Y x²

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Q: What is the annihilator for y=x e*cos 2x ?

A: Our Aim is to compute the annihilator for y=x ex cos 2x -(i)

Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y=. cos x…

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Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: 2 d So (x + 2)²0 Using Trapezoidal method spaces) dx for n=4 is equal to Blank 1 (use 2 decimal…

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Q: 1. ²₂(x² − 2xy² + y²³) dx dy

A: Solve the following integration .

Q: evaluate the limit and simplify. Complete solution.

A: Evaluating the limit

Q: dx Transforming S using miscellaneous substitu secx + 1 A S²= 2-2z² -dz 1+z² 1+z² B 1-z² 1-z² © √ 1…

A: