Derive: y = (5x-2)(2x + 3)-²

Q: 6. 7 [sin¹ 3xdx

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Q: Which of the following equations correctly states the Product Rule of Differentiation? dy = = f(x)g…

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Q: dy = 26² Q2/B) Solve the following differential equation by using homogenous D.E method dx

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Q: Question Define R as the region bounded by the functions f(x) = ez and g(x) = 1 between x = 0 and x…

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Q: dx (5-4x-x²) 18. 8. f

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Q: y= 3x²-1 2 2x+5

A: Given problem:- y=(3x2-1)/(2x+5)   Find derivative using quotient or product rule

Q: Evaluate A B с D S= 3x-5 3x4 + 6x3-3x2 - 6x x² - 4x 2 x² - 2x 2 x² - 4x 2 x2-2x-In (x-1) 1/6(x+2)…

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Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: Given

Q: Covered topics are Applications of Definite Integral: Plane Areas and Areas Between Curves and…

A: We have to find volume generated by given condition.

Q: The position of a particle moving along the z-axis is given by s(t) = 3t2 +5. Use difference…

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Q: 1. Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x.

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Q: Solve the given function using chain rule of differentiation. Show your full solution.

A: Given

Q: 15. cos³ 3x 3√√/sin 3x dx

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Q: 12. dx Ve -1

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Q: Timothy heard that he could triple his money in 27 years if he invested it in his friend's business.…

A: To find the compound interest.

Q: 14. sec xdx 2 3/2 (1 – 4 tan x)³/²

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Q: 20. √9-5x² X -dx

A: SOLUTION-

Q: Determine whether the lines L₁ and L2 are parallel, skew, or intersecting. L₁: x = 6 + 4t, y = 8 -…

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Q: 7. √16-e2x e* -dx

A: We can solve the integration as below.

Q: Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x. Determine the area of region…

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Q: Consider the curve, x² - y² + sin (TX) In(x) + x = 0. =

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Q: ·S. The integral of sect S S x dx x²+√√√x². sece tane de sece - 1 sec²0 do 1+tano cose de 1-sine…

A: Given Problem:-

Q: A payment of $2,300 is due in 2 years and $3,700 is due in 4 years. These two original payments are…

A: To find:The payment required 3 years for the rescheduled option.First we have to take effective…

Q: 1. y=-x²-3x+6, x+y−3=0; about y = 0

A: First, we graph the given equations using a graphing calculator.  The shaded region is rotating…

Q: The volume of a cube can be represented using the function V(s) = s³ Which formula of the sphere is…

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Q: QUESTION 16 Write the following power series in sigma notation. x² x6 1-4- 2! 3! x8 4! ...

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Q: S₁ 2 63 Evaluate: A 16 B 105 C) None 16″ D 105 2π E 63 sinxcos³xdx is equal to

A: We can find the integration as below

Q: For the function y=x√ find the values of x for which the rate of change of y with respect to x is 6?…

A: Given: y=xx ⇒y = x32 Rate of change of y with respect to x is defined as dydx

Q: Find if x-t³+1 and y=4t²-4t. d²y dx²

A: Solution of given question is written in below steps.

Q: Use Matlab Commands to solve the following exercises: Excercisel: a= b= Find i. 5a + 2b ii. |3a -…

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Q: Find y dy ·S- using the substitution +5= √√y+2 U /y+2 /y+2−5) (5√√y+2+y+24) + C…

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Q: f(x)=(6x¹-2x+1)

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Q: Let Use the limit definition of the derivative to calculate the derivative of f: f'(x) = Use the…

A: Given: f(x)=3x3-6x-4

Q: 3. fx² √9-x² dx

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Q: Define Q as the region bounded by the functions f(x) = x and g(x) = in the first quadrant between y…

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Q: Evaluate: 00+ • exdx

A: SOLUTION-

Q: By method of Integration by Partial Fractions, A B(2x-2) + C [(x³ + 5x²+6) dx ·11 + (x² - 2x + 5)²…

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Q: 3. Find the average value of the function on the given interval.

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Q: 20. S dr √3-4r-r²

A: On solving this we will get

Q: If F(x)=2x^2+5x+2,then F'(x)=4x+5.Thus,if f(x)=4x+5,then f is the___of F and thus F is a/an___of f.

A: F(x) = 2x^2 + 5x + 2 F'(x) = 4x + 5

Q: (-2-x)²+5 if x ‡ - 3 = 4x + 17 if x = -3 the following limits. Enter "DNE" if the limit does not…

A: The given function is: f(x)=(-2-x)2+5 if x≠-34x+17 if x=-3

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: fxe-*dx= 303 blow Sie f sin (In y)dy =

A: Integration by parts : ∫u·v dx = u·∫v dx - ∫ddxu·∫v dx dx

Q: 18. f(tan 2x + cot 2x)² dx

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Q: 4. y = 4x², x = 0, y = 16; about y = 16

A: Volume = ∫ πy2dx here y = 16 -4x2 and limit from x 0 to 2

Q: y" + y = tanx

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Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: (4x-2)dx x³-X² - 2x

A: We have to evaluate ∫4x-2 dxx3-x2-2x.

Q: 1= sin√xcos√x √x A) None Зл B 256 Зл C 512 3 D 256 3 E 512 -dx is equal to

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Q: = 2x tan

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