Homework 11 Parametric: Problem 5 Given ze and y = tet, find the following derivatives as functions of t. dy/dx = d'y/dr² =

Q: 3. lim x 3 (x-3) tan(9-x²) sin (2x-6)

A: Explanation of the answer is as follows

Q: What are the rectangular coordinates of the point whose cylindrical coordinates are (r = 7,0 = 1.2,…

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Q: Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the…

A: To find out the volume of revolution.

Q: The height y (in feet) of a ball thrown by a child is 1 -x² + 2x + 5 y = 16 where is the horizontal…

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Q: Replace the polar equation r = 5 csc 0 with an equivalent Cartesian equation. Then identify the…

A: The given polar form of the equation is: r=5 csc θ

Q: Σ(+6) της

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Q: 16. Let u = ln t, t = 2r and r = √w. Find and simplify du dw in terms of w.

A: As per Bartleby guideline,  we have answered only the first question. Please repost mentioning the…

Q: An ellipse of equation 4x²+2y²=k the distance between its foci 3√2 Find the value of k

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Q: An irrigation channel is constructed by bending a sheet of metal that is 3 m wide, as shown in the…

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Q: Find the exact value of sin (2θ) given that sin (θ) = 3/5 and θ is in quadrant II.

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x)=x+1,…

A: (i) Given that the tangent line the graph of the function at the given point  g(x) = (6/7) x+ 1…

Q: est to the point 2, 2

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +9 1 = lim t→+∞ (?, ?) 7t² + 8' 4t,

A: Given problem:-

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -2x - (sin(x))² Read It Need…

A: We can solve this as follows:

Q: Express the limit as a definite integral on the given interval. n lim [7(x)³ - 5x;*]4x, [2,7] n→∞ =…

A: Here, the limit of the integral is [2, 7]. Further, ∆x is replaced by dx and replace xi* by x. Thus,…

Q: A tank is full of water. Find the work required to pump the water out of the spout. Use the fact…

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Q: Graph the pair of parametric equations with the aid of a graphing calculator. (Hint: don't forget to…

A: Given data÷

Q: Find T(t) and N(t) at the given point. π r(t) = 4 cos(t)i + 4 sin(t)j + tk; t = 2 4 1 T(+7) = -√17 Т…

A: given  as you have already found Tangent vector

Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or…

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Q: (D²4)y= 8e²x - 12

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: Do as indicated. 2. Use the Squeeze Theorem lim sin (sinh x)csch x. x-18 to evaluate

A: Given problem:-

Q: Find the critical numbers of the function F(x) = x/5(x - 9)²

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Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

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Q: Find the exact length of the curve x = tsint, y = t cost where 0 ≤ t ≤ 1.

A: answer is in next step

Q: 314! What is the value of the expression 5! ? A 3 5 B 5 C 42 D 3,991,680

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: 1+/ lim x-1 2x² + x1

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Q: 3x

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Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why. a- Lim 4 c- lim…

A: See the details solution in below

Q: SCALCET9 11.5.006. Test the series for convergence or divergence using the Alternating Series Test.…

A: Use alternating series test to check the convergence of series

Q: Suppose you deposit $1000 at 7% interest compounded continuously. Find the average value of your…

A: To find out the average value of account during first 4 years.

Q: An ellipse of equation 4x²+2y²=k the distance between its foci 2√3Find the value of k

A: A detailed solution is given below

Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (5, -3), vertex…

A: The general form of the parabola is given by: y=a(x-h)2+k...(1) where (h,k( is the vertex of the…

Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

Q: Find curl F and div F given F(x, y, z) = e* siny i+ esinzj+e-² sin x k

A: Given  Fx, y, z = e-x sin y i + e-y sin z j + e-z sin x k We have to find curl F and div F.

Q: Suppose parametric equations for the line segment between (7,-3) and (8, 2) have the form: Т a + bt…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the centroid of the given region. (A) (5,15) (B) (3/22,45/61) (C) (5/14,38/35) (8/23,76/111)…

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Q: Evaluate the following limits. USE OF L'HOPITAL'S RULE IS NOT ALLOWED. 3. lim (x-3) tan(9-x²) sin²…

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Q: d³y_d²y_dy + y = 0 dx³ dx² dx

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Q: = ||r' (t) × r"(t)|| ||r(t)||³ to find (t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk Use the formula…

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Q: Find a general solution. Show the steps of derivation. Check your answer by substitution. -1.2 6. y'…

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Q: VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your…

A: Find your answer below

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² = 100 Or-10 sin 0 Or- 10…

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Q: solve for x^2y'=4x^2+7xy+2y^2 that the answer should be

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Q: Solve for the solution of: (D3 + D)2y = 0

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Q: Q₂: Find the area of the region insid the circle v=1 and the Curve r= 2 sin@ (use double integral)

A: Given r=1 and  r=2 sinθ The formula to calculate the area of the region inside the circle is:…

Q: Find the area of the region enclosed between f(x) = x² + 4x + 12 and g(x) = Area = | 2x² + x + 2.

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Q: (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C…

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