(1) What is the approximate volume of a thin cylindrical shell with height 2, radius 3, and thickness Ax?

Q: Given the function f(x) = -√√x + √³, find f'(6). Express your answer as a single fraction in…

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Q: A 1500-L tank is initially filled with a solution that contains 3000 g of salt. A salt solution with…

A: This question can be solved using the concept of differential equation.

Q: Write TRUE if the statement is correct, otherwise write FALSE. y y = h'(x) (-3,0) (3,0) x (-1,-2)…

A: To write TRUE if the statement is correct, otherwise to write FALSE. Suppose that hx is continuous…

Q: Find the curvature and the radius of curvature at the stated point. ㅠ r(t)=10cos(t)i+11sin(t)j+9tk;…

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Q: Find the limit of the trigonometric fur lim cos (5) 248

A: answer is in next step

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: The force F (in pounds) on a person's back when he or she bends over at an angle from an upright…

A: The given model is: F=0.6W sinθ+90°sin(12°) where W represents weight of the person in pounds.

Q: 17 Select the conic section represented by the equation. 4x 2 -y 2 + 24x + 4y + 28 = 0. circle…

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Q: Convert the rectangular equation to polar form. xy=14

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Q: Find the nth Taylor polynomial centered at c. f(x) = ln(x), n = 4, c = 6 P4(x) = X

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Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy?…

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Q: d d. Calculate[r₁(t) · r2(t)] and [r₁(t) × r²(t)] first by differentiating dt the product directly…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Here we have to find the area.

Q: fx-²dx

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Q: PERFORMANCE STANDARD: Formulate and solve accurately situational problems involving limits. GOAL:…

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Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

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Q: Find all values of a where the given series converges. Answer: Note: Give your answer in interval…

A: Solution is given below:

Q: [₁ [6x² arcsin(x)]dx

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Q: 2 The probability that an event will happen is . What is the probability that the event will not…

A: We need to find probability.

Q: (measured counter- 1. A circle with radius 2 is centered at the origin (0,0). For an angle clockwise…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2√x + +√x dy = Need Help?…

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Q: Write the sigma form for sin(x^2), Write the first 4 terms of the series approximation, and use the…

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Q: 7- Differentiate Y= f(g(x4)) h³(√x)

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

A: Use the ratio test for checking the radius of convergence of series

Q: Find all points of intersection of the given curves. (Assume 0 ≤ 0 ≤ 7. Order your answers from…

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Radius 5 2√3 4

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Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: d'y dx² d²y + dy dx X=

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Q: Select the conic section represented by the equation. 5x 2 + 9y 2 - 80x + 54y + 221 = 0 point…

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Q: 3. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that has a…

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Q: Cheyenne, Wyoming, has a latitude of 41° N. At this latitude, the number of hours of daylight D can…

A: Given :  D = 2.914 sin(0.017t 1.321) + 12.134

Q: Find all Max., Min., Saddle point for the functions. below: f(x,y) = x²y²-2x9 +6

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Q: Consider the function f with the following properties: f is continuous everywhere except at x = 2…

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Q: Integrating 1. y' + y = x+ Factor by Linear Equations:

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Q: On Integral of Trigonometric Functions: Determine the integral of the ff. functions. 3. sec 2 (3x +…

A: To find the integration of Functions: As per Bartleby guidelines we are supposed to answer only…

Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: More on Areas. Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence…

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Q: Convert the polar equation to rectangular form. r = 5/1+sin(theta)

A: Note that, the rectangular(cartesian) to polar conversion is given by: x=r cos θ, y=r sin θ And, the…

Q: (b) y=x-6, (1, 1)

A: answer is in next step

Q: Use the formula k(t): 390 t¹1 k(t) (4 +225 +26) = ||r' (t) x r"(t)|| ||r' (t)||³ r(t) = t²i+t¹5j X…

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Q: Radius of Convergence of a Power Series. (n!)x" Determine the radius of convergence for the series…

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Q: Solve the following differential equations of d² y dx² dx dy +3 dv −10y=3x²

A: We have to find the solution of the given differential equation.

Q: Consider the following. f(x) = - { $( (²), <1 |x|≥1 Find the x-values at which fis not continuous.…

A: We have to find the points at which the function is the discontinuous.

Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.)…

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Q: dx secx+1

A: First simply the equation Using Trigonometric identities.

Q: Write the Taylor series for f(x) = x³ about x = −2 asen(x+2)". n=0 Find the first five coefficients.…

A: Given that      f(x) = x3

Q: Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y =…

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Q: Consider the following. 5 - 10 5 -10 Find an equation for the hyperbola. Find the foci and…

A: Let's find.

Q: Find the domain and the range of the function. (Enter your answers using interval notation.) h(x) =…

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