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Q: Solve the given differential equation by undetermined coefficients. y'' + y = 5x sin(x) y(x) =

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Q: - 9y" = 27 %3D

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Q: Find the derivative of the following equation x+3 x-4 (a-4)° 2x (x-4)² 7 (x-4) 2x-1 (x–4)°

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Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: denominator is a binomial.

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Q: Solve the given differential equation by separation of variables. dy ху + бу — х— 6 dx ху — 5у + х —…

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Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 200e¬× -÷z², where T is measured in…

A: T(x,y,z)=200e-x2-14y2-19z2 The gradient of the temperature is: ∇T (x, y, z) = −200〈2x-x2-14y2-19z2 ,…

Q: Determine the angle of rotation of each shape

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Q: et +e-* find the length of the curve h(x) = from x = 0 to x = In 2. 2

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Q: 1 On which of the following interval is f(x) = continuous? - O [2, +0) O (2, +) O (-00, +0) O (0,…

A: Given,  f(x)= 1/sqrt(x-2)

Q: In x 6. lim, x

A: Solution:

Q: What is the differential equation whose solution represents the family y = Ae3x + Be 3x+Ce4x? %3D O…

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Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. π 1 sin -x cos? 1

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y2

A: Given: I=∫03∫0∞ x21+y2dydx As we know that; ∫11+x2dx=tan-1x+C And ∫a·fxdx=a·∫fxdx, where a is…

Q: 3. Find the area of the region inside the circler-3 sine and outside the limacon r= 2 - sine. Sketch…

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Q: Given y = (x + 1)(x + 2)² Find: y O (z + 2)(3x – 4) O (2 – x)(3x – 4) - O (x – 2)(3x + 4) O (2 +…

A: Apply the product rule of differentiation f·g'=f'·g+f·g' to find the derivative of the given…

Q: 10 *- 10-x (7) Solve for x. y =

A: Topic:- algebra

Q: ri(t) - r2(t)] = ri(t) × r2(t)] dt

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Q: Find the symmetric equations of the line that passes through the points (-2, 1, 0) and (1, 3, 5).

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Q: 7) FIND EQUATION Of THE TANGENT AN LINE TO THE PARAMZTRIL X=t-+もt こe AT t =0. CURVE

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Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: Given f (x) = x³ + x² + x + 1 and its derivative f'(x) = 3x² + 2x + 1, find the equation of the…

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Q: I can't understant the solution :<

A: Let, radius = r Height = h When r = 8, then h = 22. Using this we get a relation between r and h.…

Q: Evaluate F. dr. F(x, y) = 7xi + 8yj C: r(t) = ti + V4 - t²j, -2 sts 2

A: Use line integral concept

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

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Q: E1 Fnd all of the Porst order partial derivatives Toll wing fanctions. a)そ= x+5y x Sin (y). b) fexy,…

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Q: Find the norm (or length) of v = <-2, 3)

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Q: Solve the following integrals: 1. S 7e*dx 4. S 12*+1dx 5. S-dx 2. S(5ex – 6*)dx 3. Ј 3(5)dx 6.…

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Q: Find the volume oF the solid that results when the region enclosed by the give N curves y=e ソ=o, ×=…

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Q: Eses: Find the derivatives of: 1 In sinx, 2 - sin(lnx), 3 - e-cosx 4 - /cos(3x - 1), 2 - [1+ cos(x?…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: Determine whether the series E. (-2)" is convergent or divergent. If it's n=1 convergent, find its…

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Q: Find the four second partial derivatives, Observe that the second mixed partials a z = 19xeY-10ye

A: We will differentiate partially with respect to x and y.

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: Find div F and curl F if F(x, y, z) = 3y°z©i – 3x*z°j – 3xy*k. div F= curl F=

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 13 r(t) = t²i + t'"j K(t) =

A: Find k(t).

Q: 5. Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 – x} about the x-axis.

A: Surface area

Q: fast is the area of the rectangle changing at the instant when the other side is 12 cm and…

A: Topic:-  application of derivatives and geometry

Q: Solve the following differential equation step by step! y" – 2y' + y = x² + 1

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Q: Evaluate the following limit: lim x→2+ x – 2 O No answer text provided. |- 1/2

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Q: Find the first partial derivatives with respect to x,y and z. f(x. y.z) - 3x°y - 9 xyz + 10 yz %3D

A: Find first partial derivative

Q: 5: A party planner is trying to hang a sign between a house and a palm tree for someone's birthday…

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Q: Find the arc length of the graph of r(t) = = ev2'i + e¬V2'j+ 2tk, 0<t < v2 ln 7 NOTE: Enter the…

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Q: (2x – 3y) dx + (2y – 3x) dy

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Q: sin? (x) cos (x) dx

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Q: (D² + 4)y=12; y(0) = 0 , y'(0) = 2 %3D

A: (D2+4)y=12

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 3. f(x) = v2…

A: If function 'f' is differentiable at x=c the f'(c) is the slope of the tangent of the function at…

Q: The water level in a glass decreases 0.4 cm each hour due to evaporation.  At the beginning of the…

A: The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the…

Q: Evaluate -5x lim,→0 tan x O -5 O 1 O 5

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