J 6t³ cos (t¹) dt

Q: ind y" if y tan x. A] 2sec²x tan x D] 2 sin x + 2 cos x [B] secx tan x [E] sec x tan²x [C] 2 cos x…

A: y=tan(x)    ddx(  tanx ) = sec2x

Q: How much do the volume of a sphere change with respect to its diameter at the instant, and the…

A: Recall: Volume of sphere, V=43πr3

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A:

Q: Solve the equation with homogeneous coefficients. (x² + 3xy + y²)dx - x² dy=0

A:

Q: √√√x²-4 S 3 x³ X - dx

A: Given integral:- ∫x2-4x3dx

Q: Which function is increasing? Ⓒ y = ln x O y = -lnx O y = -log₂ x ****

A: Which function is increasing?

Q: x)/(x^2+1)  Use a TABLE to show intervals in which f (x) is increasing or decreasing, concave up or…

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Q: Determine whether the sequence converges or diverges. If it converges, find its limit. an = n COS NT

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Q: -5-4-3-2-1 123 1 2 3 4 5 The function graphed above is decreasing on the interval The inflection…

A: Given query is to find the interval where functions is decreasing.

Q: Find the indicated Midpoint Rule approximation to the following integral. 18 S2x² 2 27 dx using n =…

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Q: Solve the boundary-value problem y" – 12y' + 36y = 0, y(0) = 8, y(1) = 0. Answer: y(x) = Note: If…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. sin(In 41x) X dx

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Q: Solve the equation: loge (x + 4) + loge (x + 3) = 1

A: Given query is to find the value of the x.

Q: Find the vector needed to translate from point (4,1) to point (8,3). Translate (-1,2) by the same…

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Q: Determine whether f(x) = = -4x² + 16x - 2 has a minimum or maximum value, and find the value of the…

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Q: - 2q + 250, where q is the quantity Let the demand function for a product be given by the function…

A: Given,Demand Function D(q) = -2q + 250(A) Revenue from selling 105 itemsRevenue function = q ×…

Q: Ꭱ Find ff f(x, y) dA where f(x, y) = x and R = [0, 1] × [-4, -3]. SSR f(x, y) dA=

A:

Q: If lf Ŕ(t) = et cos tỉ – et sin tj Find the velocity and acceleration vectors.

A: To find the velocity and acceleration vectors for the given position function.

Q: Let y = f(x) = = e -10x ¹+1 Find the equation y = T(x) of the tangent line of the inverse of fat (1,…

A: Given that , y=fx=e-10xx4+1 find the equation of the tangent line of inverse of f at 1,0.

Q: 2. (x-2) y = y+2(x2) دعا 3

A: Given x-2y'=y+2x-23

Q: Given: y = 5 (cosh log )², find y' (cosh² O g = =|sinh 2 log = ]5 sh®log }} O 5 O ý =−}(m& )[sinh 2…

A: The objective of the question is determine the derivative of the given function and choose the…

Q: 3. fxe (4-x²) dx

A: ∫ xe4-x2dx

Q: Prove the identities sinh(2x)=2sinh(2)cosh(2)

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Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

A: Given query is to find the derivative of the function.

Q: If f(x) = x5 + x + 1, find (ƒ−¹)′(3). Note: The point (1,3) is on the graph of f. [B] 1 [E] ¹ 6 [A]…

A: Given query is to find the value of indicated function.

Q: Put the equation y = y = - 3(x + 2)² + 5 into general form y = ax² + bx + c.

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Q: Find the derivative of: - R(t) = (sin² (3t+1), ln(t² − 1), ²) +1

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Q: 3. On what intervals is h(x) = x² - 10 arctan(x²) increasing and on what intervals is it decreasing?

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Q: x + 3y s 18 2x + yΣ 14 x Σ Ο Υ Σ Ο

A: See this solution in below.

Q: 3. sin² 3xdx

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Q: Give the appropriate form of the partial fraction decomposition for the following function. 3x…

A: Topic -Partial fraction decomposition We are given, 3x(x-1)2(x2+3)

Q: Question 29 Given 3x7 +825 - 21. determine, y' 630x +480x² + O 2520z³ +960x O 840x³ +360 P DE 126…

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Q: 2 y=5 + x3

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Q: Find the indefinite integral using the substitution x = 5 tan(0). (Use C for the constant of…

A: Topic- Indefinite integral We are given,∫x525+x2dxx=5tan(θ)

Q: Use logarithmic differentiation to find the derivative of y = (In(4x))(5x) (where x > 1/4 so that…

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Q: 2. Determine f'(x). (a) f(x)=√√26 (b) f(x) = 26√T (c) f(x) = √26x (d) f(x) = √26.x

A: To find the derivative.

Q: [(x² +1) cos +=dx 2

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Q: 4. Find the measurements of a box shipped via USPS that will maximize the volume in order to give…

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Q: 1. Determine the equations of the tangent and normal lines at P(1,1) given x³y - 2xy² + x² - 3y + 3…

A: To determine the equations of tangent and normal to the given curve.

Q: 3. For Z= xtanxy,evaluate Zyy

A: The given function Z=x tanxy We have to find Zyy.

Q: Evaluate the following integral using trigonometric substitution. 7x² dx (121+x²)² S What…

A: The given integral is 7x2(121+x2)2.

Q: What else do you observe? Concept Check: Evaluate the following integrals: ·S 4. 5sin2x cos2x dx…

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Q: b) Is the integral in de convergent? Explain why! I

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Q: 3. Let f(t) = t(1 - 2t). a) Find the average rate of change of f(t) with respect to t as t changes…

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Q: What term(s) should appear in the partial fraction decomposition of a proper rational function with…

A: Topic - Partial fraction decomposition We are given, a.) A factor of x-3 in the denominatorb.) A…

Q: By using the definition of the derivative, one can sin(x) - 1 x-x/2 2x - R Identify the correct…

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Q: Use the implicit function theorem; dz/dx = -Fpartialx/Fpartialz to find dz/dx and dz/dy…

A: Given expression: ln(2x3+2y6+3z5)= 14+12xyz Let f(x,y,z) = ln(2x3+2y6+3z5)- 14-12xyz We know that…

Q: Find the cross product axb Where a = <-4₁0₁22 and 6= (-2, 5, -27. laxb-CD, Find the cross product…

A: In this question we have been given two vectors and we need to find their cross product.

Q: Find the absolute maximum and absolute minimum values of the function f(t) = √t · (3 – t) on the…

A:

Q: etermine whether the sequence converges or diverges. If it converges, find its limit. n+1 an = 1.

A: Given query is to find the limit of the expression.