The radius of a circle is increasing at a rate of 2 ft/min. At what rate is its area changing when the radius is 3 ft? (Recall that for a circle, A = ²².) ft²/min

Q: 5. Consider the surface obtained by rotating the graph of f(x) = 1/2, 221, around the z-axis. This…

A: We will show this using integration ∫1∞1xdx = ln x1∞ = limx→∞ln x = ∞

Q: ∫ sin4x dx

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A: Given

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A: convert degree to radian

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Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

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Q: Write the equation of a sine or cosine function to describe the graph. 'y 0 2π 2π 3 7 6+ 5 4 3 2 2π…

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Q: -The Bernoulli's form of the differential equation 2x'dy-y(y² +3x)dx=0 is

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Q: 3. In evaluating the integral S fractions. Let x² dx (x-1)²(x²+1)' you will decompose x² dx…

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Q: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: ∫(4x3−12x)(x4−6x2)−3 dx Evaluate indefinite anti-differentiation

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Q: (3x+4)2dx Evaluate indefinite anti-differentiation

A: The given integral is (3x+4)2.

Q: A circle has a radius of 3.5in. A sector of the circle has a central angle of 1.5 radians. Find the…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² − 3)i+tj; t=3 T(3): N(3) = =

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Q: Suppose that the point P can be placed anywhere on the line segment AB in order to change the angle…

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Q: second derivative of y with respect to x from the parametric equations given 4) x=√1-t₁y = t³ - 3t…

A: We can find the required 2nd derivatives as below

Q: Let f(x) = 5 on [−3, 1]. x+5 Find all numbers c in [-3, 1] for which the derivative is equal to the…

A: We are given a function f(x) = 2/(x+5) on [-3, 1].   We have to find all the c in [-3, 1] such that…

Q: 1 x² + 8x + 5 x3 + 12x2 + 15x + 6 dx

A: Solution of given question is written in below steps.

Q: A plane flying horizontally at an altitude of 3.4 miles and at a speed of 790 mi/hr passes directly…

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

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Q: Find a simple closed curve Cwith counterclockwise orientation that maximizes the value of { v²dx + (…

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Q: Consider the following series. Σ» (#1) (a) Determine whether the series is convergent or divergent…

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Q: 3. Determine whether each geometric series converges. If the series 7n+1 2n converges, find the sum.…

A: Let's find.

Q: dx x√√x4 - 4 S

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Q: Calculate[ri(t) r2(t)] and [ri(t) x r2(t)] first by differentiating the product directly and then by…

A: r1(t)=6t i+ 4t2 j+ 4t3 kdr1dt=6 i +8t j +12t2 kr2(t)=t4kdr2dt=4t3 k

Q: Use the formula k(t) 286 +⁹ k(t) = (4 + 169 +¹2) ² = ¸ ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) =…

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Q: s dx x+√2x+1

A: Let  2x+1=u ⇒dudx=12x+1 ⇒dx=2x+1du also x=u2-12  ∫dxx+2x+1=2∫uu2+2u-1du…

Q: Evaluate 1.1² (2x − y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (3, -5)

A: Solving

Q: Find the equation of the tangent line to the graph of f(x) = x'e- at x = 0.

A: The given function is f(x)=x9e-x at x=0.

Q: compute the area of the surface formed when f(x) = x3 between 1 and 3 is rotated around the x axis

A: Solving

Q: Two years ago, $5, 000.00 was placed into an investment in which the amount of money present, P,…

A: To find the amount of investment after 15 years from now.

Q: 343 2 1. y = x² - 9 and y = x + 3 (Answer: 6 s. u.)

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Q: Verity Green's Theorem by evaluating both integrals ƏN [x² dx + x² αy = [] (2 - 0) A √y² dy dA ax ду…

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Q: Use Stokes' Theorem to evaluate for F. dr. F(x, y, z) = 5xyi + 5yzj + 5zxk C where is the triangle…

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Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where…

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t = T() 6 37 0, √/3 X N…

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Q: 2. 2 ydx + x(x² In y-1)dy=0

A: Solution is given below:

Q: Find Ay and f '(x) Ax for the given function. y = f(x) = =, x = 4, and Ax = 0.5 O-0.02778; -0.125 O…

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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…

A: We have to find the value

Q: 15 Find sin 2x, cos 2x, and tan 2x if cosx = 17 and x terminates in quadrant I.

A: Given that  cos x = 1517 and x terminates in quadrant I. We have to find  sin 2x, cos 2x, and tan…

Q: Use the given derivative to find all critical points off, and at each critical point determine…

A: Follow the procedure given below.

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

A: r(t)=cos(πt) i -ln(t) j+t-12 kDomain of:cos(πt): no restrictions.(-∞, ∞)-ln(t): defiend for…

Q: Use the given derivative to find all critical points of f, and at each critical point determine…

A: Given :

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t)||³ to find k(t). r(t) = 7 cos(9t)i + 7…

A: Let's find.

Q: * Using trigonometric substitution to evaluate: find dx √ dx, √2x²-4x-7 (3√2)/2 cosø dø O (3√2)/2…

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Q: Solve the following Bernoulli's differential equations. 1. x²y' + 2xy-5y³ = 0

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Q: (8x4 − 5x2 + 2)dx evaluate indefinite anti-differentiation

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Q: Describe the graph of the equation. r = (8-2) 1+ 14tj It is a line in 2-space through the point…

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