Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0

Q: find the derivative and simplify the answer sin² (esin t) + cos-{(2t3 – 5)

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Q: e-2 1 Evaluate: e-3 xInx Oc -In 6 O d. In 6 2/3

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Q: Give the VALUE only. No need to include the unit. * Let s, =15r +10r +20 and s3 = 5t + 40f , t 2 0,…

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Q: I c exists in (0, 1) such that f(c) (1)- f(0) 1-0

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Q: 22 – 9x? = 1 4.

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Q: Q2) Convert the polar function r = tan20 to cartesian

A: We know that x = rcosθ, y=rsinθ Given: r=tan2θ

Q: 2 dr sech 2r= e2r +e-2r A) True B) False

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Q: Consider the parametric curve defined by x=3+5t and y=1+31 Over which values of , does the curve has…

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Q: Obtain the general solution unless otherwise instructed A. LINEAR EQUATIONS WITH CONSTANT…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: Note Answer One Question Q1 The following data is provided for the velocity of an object as a…

A: Let's find.

Q: nsider Evaluate дхду

A: Given,             z=ex3+y2To find : Evaluate ∂2z∂x∂y

Q: : / yº sech(e™mv) tanh (» ) dy 7lny Evaluate: @ -ch(7) + C None

A: Given problem:- ∫ y6 sech(e7ln(y)) tanh(e7ln(y)) dy

Q: r= sin E-0) in first quarter.

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Q: 4 r4-y Evaluate triple integral , S S dz dy dx -2

A: We have to evaluate the triple integral  ∫-22∫x24∫04-ydz dy dx.

Q: Q3) Evaluate triple integral dz dy dx.

A: A detailed solution is given below

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: 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: Is Rolle's theorem valid for the function f(x) = V1- a. Yes. It is valid in this range b. No. It is…

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Q: O Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2, y =

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Q: 1' 1 3 (e) Show that 5 k=1 k k+2

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

Q: Evaluate: / yº sech(eThy ) tanh (e "hy ) dy 7Iny -mch(v^) + C None -ech"(,?) + C

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Q: Consider the region bounded by the curve v= x2 – 1 and the x - axis over the interval [0,3]. Find…

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Q: Let f(x) be the function 11a - 5x+4. Then the quotient f(8 + h) - f(8) can be simplified to ah + b…

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Q: Find the value of e which is defined as the angle between j+k and i+j_ None of the choices 4 프2 프3

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

A: Here we have to solve the given differential equation x2dy+3xy-1dy=0 ............................…

Q: .2 dx I (w² – 25)5/2

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Q: Each of the regions A, B, and C enclosed by the graph of f and the x-axis has area 6. Find the value…

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Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

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

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Q: 02) Solve the D.E dy - (2x/1-y2)dx 0

A: The given differential equation is dy-2x1-y2dx=0

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

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: 1. Find the indicated limit or state that is does not exist lim (3x'y- xy³) а. (x,y)→(1,3) b.…

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

A: Here we have to use the trigonometric subsitution method.

Q: Given Ax) = - 2 use the first principles definition to find f'(1).

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Q: Evaluate: (cosh²2r+ sinh²2r) dr A r +C -sinh 4r +C 4 B (c) None - sinh 2r + C 2r +C

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Q: Consider the series 5 + 9 + 13 + How many terms does it take for the sum to be 860? O 21 O 20 O 19 O…

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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 the speed at the given value of t: r(t) = (e4, -9,4t-1),t = 4

A: We know that V(t)=r'(t)Here r(t)=<et-4,-9,4t-1>Differentiate…

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

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Q: 10 if f(x)= t +P, then %3D f'(X) = f'(-2)=

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

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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: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: We have to slove differentiable function above question

Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

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Q: 5.Find all the first partial derivatives of each function f (x,y) =(2x– y)* а. 3/2 S(x, y)= (4x–…

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

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin (* + 0) in…

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

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