irvature and the radius of curvature at the stated poi r(t) = 6 cos(t)i +6 sin(t)j+ 7tk; t= 2 r the exact, simplified answers.

Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of does the curve has a…

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Q: Find y' if 4 cos x cos y = 3y. %3D

A: To find the derivative.

Q: Consider Evaluate ( 3x² + 6x ) e *+2) (6x2+ 3x) e +y2) (6x+9x)e+y2) O (9x4+6x) e *+y2)

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Q: Find the volume of the solid that results when the shaded region is Y = x revolved about the…

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Q: Question 12 S dy =2/y- 5inlVy+5|+c Vy +5 A True B) False

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Q: EValuate J s 2'as O a. 2*(sln2 – 1) (In2)2 O b.2(sln2 - 1) (In2)2 O C. 25 sp.7s (1 – Zu). + 1) In2 O…

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Q: Please answer the question below: Explain in detail which test you are using to determine…

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Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: Option A is true

Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

A:

Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 1 - x dx 2. y =

A: To evaluate the given integral.

Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0

A: Let's find.

Q: Find (a) if fx) = /x-a+1.

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Q: Evaluate (s 2'ds Oa 2 1) In2 Ob. 2 (sln2 - 1) (In2)2 O. 2(sin2 - 1) (In2)2 Od 2° +1) In2

A:

Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 Ju. (v x w)| to determine…

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Q: Q3) Evaluate triple integral , dz dy dx.

A: ∫-22∫x24∫04-ydz dy dx∫dz=zSubstitute the limits=4-y-0                              =4-y

Q: Q2) Solve the D.E dy - (2x/1– y²)dx = 0

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Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

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Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x-0, y= 0,…

A: Given problem:- Find the volume of the following solid.   The tetrahedron bounded by the…

Q: 8. If f (x,y,z) = 3x²y – xyz + y²z? _Ifind each of the following: f. (x, y, z) b. f, (0,1,2) а.

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Q: 1 dt. o t4 +5 Let f(x) = Find the derivative f'(x). e2x none of the choices et

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = %3D

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 6 Y 4 6. 10 10 8

A:

Q: Water is pouring into a swimming pool. After t hours, there are t + sqrt(t) gallons in the pool. At…

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Q: Find h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

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Q: Use the Midpoint Rule for the triple integral to estimate the value of the intergral. Divide B into…

A: Note that, 0≤x≤4, 0≤y≤8 & 0≤z≤4 generate the cube. And, the mid-points of the cube are:…

Q: 9. (D² – 2D + 5)²y = 0 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = –4 %3D -

A: We will solve auxiliary equation then we will find the solution.

Q: QI) Evaluate the integral dx dy using polar coordinate

A: Solving

Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 + x – 2

A:

Q: Find the value of dt Oa 40 Ob.53 Oc 23 Od.13

A: ∫0∞e-3tdt∫e-3tdtSubstitute u=-3t→dudt=-3→dt=-13du=-13∫euduWe know that ∫axdx=axln(a)=eu

Q: The limit represents a derivative f' (a). Determine f(x) and a. 14h lim 1 h→0 (Express numbers in…

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Q: Q3) Find the Area bounded by the curves y? = and x = 2y – y².

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Q: Q3) Evaluate triple integral S(x2 -y?)dz dx dy.

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Q: Evaluate the integral: (3si + 9s²j + 4k) ds

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Q: Find the volume of the solid formed by revolving the region enclosed by the closed curve 4x² + 9y² =…

A: As per given  We have to determine volume of solid

Q: 1 et dx 1 (1 — е*)2

A:

Q: 1. The graph of a function y = a/b(x-h)+k shown below. -1 -40 Algebralcally determine two different…

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Q: Consider the integral 5 x (z° +1) dx. In the following, we will evaluate the integral using two…

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Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0 %3D

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Q: Find volume of body bounded by z 0 from below and z = 4 - y from above inside y = x2 ,y = 4 .

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Q: dy -by implicit differentiation dx Given 4x -9y =1. Find

A: 4x2+9y2=1

Q: Solve the D.E dy -(2x /1-y2)dx = 0

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Q: Q2/ Fit a second -order polynomial to the data in the following table: 5 1 4 2 Y 2 8 3 4 -1 4 6.

A: We need to find quadratic equation.

Q: dy Find the general solution of 2x² = a? + y? dx %3D

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Q: Let 1. f(x) x+1 Use the limit definition of the derivative to find (i) f'(-4) = (ii) f'(- 2) = (i)…

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Q: Question 5. Find the Laplace transform of the following function by using the integral definition of…

A: Given problem:-

Q: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

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Q: 8. (a) Use the limit comparison test to determine whether the series converges. k=1 (b) Use the…

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