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- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?A tank contains 1300 L of pure water. The solution that contains 0.01 Kg of sugar per liter enters the tank at the rate of 7L/min. and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the beginning? y(0)= to( Kg (b) Find the amount of sugar after t minutes. y(t) = (kg) (c) As t becomes large what value is y(t) approaching? in other words, calculate the following limit lim t-oo y(t)= (kg)Find the limit (if it exists). (If an answer does not exist, enter DNE. Round your answer to four decimal places.) lim x→7+ ln(x − 7)
- a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary. b. Confirm your estimate in part (a) with a proof.limx → 1 (x-2) / (x-1)2 how do I calculate the following limit without using the L'Hospital's ruleEstimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→0 x − 3 x − 1
- Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞ 6e−6xFind the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) lim x→0− (6+1/x)If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account is v = (mg/c)(1 − e^(−ct/m)) where g is the acceleration due to gravity and c is a positive constant. A. Calculate lim(t→∞) v. What is the meaning of this limit? B. For fixed t, use l’Hˆopital’s Rule to calculate lim(c→0+)v. What can you conclude about the velocity of a falling object in a vacuum? *I missed a lecture on this topic, so more detail/explanation would be great!*