Given: vector-valued function Ř(t) = (3 cos 2t, 9t, −3 sin 2t) 1. Reparametrize R using the directed arc lengths from the reference point P(3, 0, 0) in the direction of increasing values of t.

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A: The given function is  f(x)=x3+x2+x+1

Q: At 12:00 noon, there were 225 bacteria present. By 4:00 pm, there were 427 bacteria. If the bacteria…

A:

Q: 10. Find the equation of the curve whose slope is the inverse of the sum of the square root of five…

A: Given ,  We have to find the equation of the curve whose slope is the inverse of the sum of the…

Q: 6+ З +2 (2x+1)= 8

A: 6x3 + 2(2x+1) = 8 2x + 4x + 2 = 86x + 2 = 86x = 8 - 26x = 6x = 66 = 1

Q: 9 Use the shell method to find the volumes of the solids generated by revolving the shaded region…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: d) Find s' (t) for the function. s(t) = 3t² + 5et

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Q: Jo dx 0 1-x² 2 e) fx√x² + 1dx (Hint: use a substitution)

A: Use substitution to solve

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A:

Q: 4. Evaluate the following limits. a. lim X→→→+** 2x 3x² b. lim c. lim -3/x X In5 x x²

A: This is a problem related to limit calculation. Based on the general formula and concepts we will…

Q: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

A: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

Q: Find the exact values of inverse trigonometric expressions for Parts a to c in radians. Sketch the…

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Q: Find the volume of the solid generated by the revolving Shaded about region the 7-axis 1 0.5 X =…

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Q: Find the extrema of each given function on a specified closed interval. 1.) g (x)= x³ - (3/2)x²,…

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Q: 2-201 0 1 1 1 103 A = 0 1 -1 3 0 1 1 1 1 1 1 Which is the element A3,2?

A: To find the element A3,2  of the given matrix A.

Q: Find the gradient of the function g(x,y) = xy² at the point (3, -1). Then sketch the gradient…

A: Given:        Function gx,y=xy2   The gradient of function                  ∇gx,y=gx,gy   Taking…

Q: The area of the region bounded by the curve y = x² and the line y = 16 64/3 256/3 128/3 32/3

A: Given :   y=x2 y=16

Q: Problem 2. Consider the equation z = x² + y² + 1 A. Find the equations for az- and yz-traces. B.…

A:

Q: The are of the parabola y=x² from (1, 1) to (2, 4) is rotated about the y-axis. Find the area of the…

A: Let's find area of the resulting surface.

Q: дz дz Suppose z is a function of r and y and tan(√x + y) = e²². Determine and 3x ду

A: given function tanx+y=ez2

Q: ou make an investment of $4,500 and the investment loses a continuous 5% each year, what will the…

A: Given query is to find the value of investment after 15 years.

Q: 10 = (+5x)dx 45x+9 -1 7/4 52 (+9) + 48 (x+g)' f(x+9) + 2

A:

Q: 17. What is the amplitude of the graph y = -4sin (x - 2)? The amplitude is units. 4 02 2π K|2

A: Given problem :- 17. What is the amplitude of the graph y = -4sin (x - 2)?

Q: f) Use L'Hopital's rule to evaluate: sin x lim X-0 X

A:

Q: Find the equation of the tangent line to the function f(x) = 5* at x = 4. (Use symbolic notation and…

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Q: 6) (-2√2,2√2) 3 3√3 8) 2 10) (-2,-2√3)

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Q: 1. Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2…

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 ex cos (yz),…

A: Topic:- application of derivatives

Q: xy a. Compute the first- and second-order partial derivatives of f(x, y) = xe with respect to both x…

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Q: Find the binommal coefficient (4)

A: Topic = Algebra

Q: Use the shell Method to Find the Volume of the bounded by Solid generated by by revolving the region…

A:

Q: Find values of x and y such that  fx(x, y) = 0 and fy(x, y) = 0  simultaneously. f(x, y) = 7x3 −…

A: This question is based on Partial differentiation.

Q: nd the derivative of the function at Po in the direction of A. f(x,y,z) = 5 ex cos (yz), Po(0,0,0),…

A: Given query is to find direction derivative at given point.

Q: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

Q: The displacement (in meters) of a particle moving in a straight line is given by s= t2 - 5t + 16,…

A: We want to find average velocity.

Q: Q/Use Lagrangian polynomial to find f'(2.1) from the following table x 1 2 3 17 22 f(x) 10

A:

Q: The points R(-1, 1, -3), S(3, -3, 6), T(0, 0, 10), and U(2, 4, 7) are the vertices of parallelogram…

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Q: 8.1 PLEASE TYPEWRITTEN FOR UPVOTE. SHOW YOUR COMPLETE SOLUTION.

A: To find out the family of curves whose slope is given.

Q: What is the period of the graph below? sto 8+ 7+ 6+ him

A: As we can see graph  Function repeat his value after every 4 point .

Q: Find the Area under a curve y = 4-x² from x = -3 to x = 3

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Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

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Q: 5. Find the limit using any method of choice. x + 2 lim x-2 2x² - x - 10

A: A detailed solution is given below.

Q: Determine the limit of the sequence or state that the sequence diverges. an = 1 6 n² (Use symbolic…

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Q: 12. Find the integral of S (x². √(x² + ² =) dx

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Q: sin² x lim 0-x X

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Find L(e³t cos 2t) Your answer with CamScanner

A: A detailed solution is given below.

Q: [x³√₁-x² x2

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Q: Find the equation for the line tangent to the curve 2exy = x + y

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Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

A:

Q: HOW DID YOU GET THE ANSWER??

A: Let's find general equation of circle.

Q: sec x = Let f(x) + x³e² - log₂ (5x + 1) + 1 x² √T Using the derivative rules learned in our course,…

A: