Solve the initial value problem for r as a vector function of t. dr Differential equation: Initial condition: r(t) = ₁+₁+k i+ dt = -7ti-5tj-tk r(0)=2i+j+7k

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A: let A, b and h be the area, base and height of the rectangle

Q: The Intermediate Value Theorem works for f(x) as long as f(a) and f(b) exist. O True O False

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Q: Consider the following function and its graph. 3(x + 1)³(x + 9) (x - 5)²(x+4)² f(x) = (b) -10 (c)…

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Q: Consider the vector field F(x, y, z) = (4z + 2y)i + (4z + 2x)j + (4y +4x)k. a) Find a function f…

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Q: 1- Evaluate the limit. a-Limx²-4/(x²-x-2) X-2 c- lim {3x-5 X-8 b- lim [(x+20)¹/2+25] /x+5 x→5 x<8…

A: to determineall limits

Q: 9. Evaluate the integral or show it diverges 1 S₁² 2x²=6 dx

A: As we know that The logarithm of a negative number is undefined Given integral

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Q: The local maximum of the graph below on the interval [-1,2] happens at the point where x = -1: PA -3…

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Q: Evaluate the following limits. If needed, enter inf for and -inf for -∞ DO NOT enter decimals enter…

A: given limit

Q: Suppose the daily supply equation for noise cancelling wireless headphones is given by p = S(x) = 70…

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Q: Find the integral or state that it cannot be evaluated by our substitution formulas. (If it cannot…

A: we have functionx (x5-8)1/3.  We have to integrate it by substitution

Q: 10. Σ n"x" Σ

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Q: The vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot is shown in…

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Q: = A lune occupies the region inside the circle x² + y² = 8y but outside the circle x² + y² Assume…

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Q: Determine if the statement is true, false, or cannot be determined. Assume that the point (a, f(a))…

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Q: 4. (-9) h()== In dx

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Q: Find the maximum and minimum values of f(x, y) = 2x + y on the ellipse x² +9y² = 1 maximum value:…

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Q: 4. Evaluate the following definite integrals using geometry. 3 >-{³ (a) f(x)= x <3 x 23 f(x) dx =

A: As per the Bartleby guidelines, answer only first question as the other questions are not the sub…

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A: If the marginal cost for a product is  and the production of 10 units results in a total cost of…

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Q: Solve the triangle, rounding to the nearest tenth, assuming a is opposite side a, § is opposite side…

A: a²=b²+c²-2bccosA

Q: Evaluate using integration by parts. І 0 5xe4x dx

A: The given definite integral .The aim is to calculate the integral value.

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it (your…

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Q: A television camera is positioned 4,000 ft from the base of a rocket launching pad. The angle of…

A: Solving the problem

Q: From curve equation y=x²-2x+1 at (2,1) Find ?

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Q: Give a geometric description of the set of points in space whose coordinates satisfy the given pairs…

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Q: 1. Find div F and curl F if F(x, y, z) = 8e™ i − 10 cos y j + 10 sin² z k. div F= curl F=

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Q: 10-Determine the intervals of increase and decrease for the function f(x) = 2 cosx + (3)1/3 x on the…

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Q: Show that the series Σ=1 (-)" is convergent. How many terms of this series do we need to find the…

A: We have to show if the series converges and find the minimum number of terms required for the sum…

Q: Suppose that the proportion P of voters who recognize a candidate's name t months after the start of…

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Q: Find a function f(x, y, z) such that Vf is the constant vector (5, 6, 5). (Use symbolic notation and…

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Q: Write a polar equation of a parabola with the focus at the origin and the vertex (r, 0)=(5, 1). O 7=…

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Q: A math tee shirt business is expected to generate $45,000 in revenue per year for the next 5 years.…

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Q: Suppose that for a particular product, the number of units x produced per month depends on the…

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Q: Evaluate. b a 2e³t dt

A: Given Integral

Q: (

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Q: If the demand function for math anxiety pills is p = D(x)=√√25 - 2x, determine the consumer surplus…

A: Given the demand function:

Q: The demand and supply functions for Penn State women's volleyball jerseys are: p = d(x) = -x² - 23x…

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Q: Determine if the statement is true, false, or cannot be determined. Assume that the point (a, f(a))…

A: given that f'(x) is negative at x=a then f(x) is decreasing at (a, f(a))

Q: When a raindrop falls, it increases in size, and so its mass at time t is a function of t, namely,…

A: Given:The rate of growth of the mass (m) is km(t)where k is some positive constant.That is And also…

Q: average cost as production goes from 100 units to 101 units. X

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Q: Find the absolute minimum and maximum values of f(x)=lnx- Justify your answer. 12/02 1 on the…

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Q: Find the area of r=e^(-θ/12) between π and π/2.

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Q: Utilize cylindrical coordinates to calculate ſ zdV when E is above the paraboloid E z = x² + y² and…

A: Using cylindrical coordinates, we can evaluate the integral.

Q: A baseball player hits the ball and then runs down the first base line at 17 ft/s. The first baseman…

A: The solution is shown in step-2

Q: - Applications of Definite Integrals Course Packet on income streams and annuities A Math 110…

A: The future value after t years compounded continuously is given as follows

Q: Use the Root Test to determine whether the series convergent or divergent. Identify an Since lim n =…

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Q: Use the Root Test to determine whether the series is convergent or divergent Σ 8(1 + 1)^² n = 5…

A: The given series .The objective is to check the convergence of the series using the root test.

Q: If the total cost function for producing x lamps is C(x) = 480 +37x + 0.3x² dollars, producing how…

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