In Problems 9–28, find the value of each improper
26.
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- 5. Solve: (1 + + In x + dr = (1 – In x) dyarrow_forward7.The rate of contamination in a certain lake is C ()=tIn(2/) hundreds gallons per month, where t is the number of months since the observation began. Answer the following: a) Find the total change of contamination C(t) (in gallons) between months t-1 and t-4 by using integral calculus, b) Find the time t-T such as the total change of contamination C between t-0 and t-T equals zero.arrow_forwardIn Problems 7–16, use a table to find the indicated limitarrow_forward
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- 1. Suppose that a particle moves according to the law of motion s(t) = 4g, t≥ 0. (a) Find the velocity v(t) at time t. (b) Find all values of t for which the particle is at rest. (c) Use the interval notation to indicate when the particle is moving in the positive direction and when it is moving in the negative direction. (d) Find the total distance traveled during the first 5 seconds. 2. Newton's law of gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is F = GM, where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr (What does the minus sign mean?) (b) Suppose it is known that earth attracts an object with a force that decreases at a rate of 2N/km when r = 20000km? How fast does this force change when r = 10000km? 3. In the mysterious lost city of Mim, the length of daylight (in hours) on the tth day of the year is modeled by the function L(t) = 12 +3 sin((t-80)). Use this model to compare how…arrow_forward6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 х* + 5x + 2 if x1arrow_forward9. The rate at which the value, V, of a painting changes t years after it is completed is given by the function RV(t). (a) If RV(t) + 4t + 10 (in dollars/year), what is the net change in the value of the painting from 1 year after it's completed to 4 years after it's completed? |6t + 2 (in dollars/year), give a lower estimate for the net change in the (b) If RV(t) value of the painting from 1 year after it's completed to 3 years after it's completed using a Riemann sum with 6 rectangles.arrow_forward
- 2. How much material passes in the time interval [0,/2] through the points (a) x = 0, (b) x = π/2, (c) x = -1/2? What does the sign of your answer (positive/negative) mean?arrow_forwardIn Problems 1–6, find each limitarrow_forward8. Solve for x to the nearest hundredth. [show all work] 3* = 5arrow_forward
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