# calculus

## 1) An object initially at height ‘ h ‘ above the ground is held stationary. The object is then released and falls down to the ground. a) Draw two x vs t graphs showing the motion of the object. The first graph should have down as the positive direction and the second should have up as the positive direction. b) In the situation above, the object is given somegnitial non-zero speed vo toward the ground. Draw v vs t graphs for the motion ot the object as it falls to the ground, again one should be down positive the other up positive. 2) An object initially at position r=3x+4y with velocity v0=2xβ2y experiences an acceleration given by a=1x+1y over 13 seconds. If positive x represents the direction ‘right’ and positive y represents ‘forward’; describe how this motion would appear to an observer stationary at 0,0 . Your description can be mostly natural language or drawings but you must give a value for the final velocity of the object. 3) An object is launched from height 0 with a velocity of 20 m/s at 40 degrees above the horizon. A wall is placed 10 m horizontally ahead of the object. a) Draw the height vs time graph for this motion. Make sure to label your axes, list units and scale and mark the height at which the object impacts the wall. The value of the impact height must be listed. 4) An object is dropped from the top of a 30.0 m tall building. Compare the amount of time it takes for the object to fall the first 10.0 m to the last 10.0 m . You may neglect air resistance. Precision in your communication is important. 5) A cannon can fire a projectile with a generic initial velocity of v0. Assuming a flat field with no obstructions, the longest horizontal distance is achieved at a firing angle of 45 degrees. Use physics based arguments to explain why 45 degrees provides the maximum horizontal distance.

EXPERT ANSWER In This question we have to draw x-t & v-t graph

## The total cost, TC, of producing 100 units of a good is 600 and the total cost of producing 150 units is 850. Assuming that the total cost function is linear, fi nd an expression for TC in terms of Q , the number of units produced.

The total cost, TC, of producing 100 units of a good is 600 and the total cost of producing 150 units is 850. Assuming that the total cost function is linear, fi nd an expression for TC in terms of Q , the number of units produced. EXPERT ANSWER

## Given the constant elasticity demand function as : π = ππ π π€βπππ π ππ  π‘βπ πππ π‘ππππ‘π¦ ππ ππππππ a. Show that Marginal Revenue of this function is proportional to the price (let πΎ = ( 1 π ) 1 π β ). To simplify the equation. b. calculate the Marginal Revenue when πππ’πππ = π = β2 and when b=-10. c. what does your answer mean in terms of revenue facing the firm? d. If π = βπΌ what would this imply for Marginal Revenue and Total Revenue of the firm. e. Explain how Marginal Revenue and profit maximization would be affected if demand was inelastic.

Given the constant elasticity demand function as : π = ππ π π€βπππ π ππ  π‘βπ πππ π‘ππππ‘π¦ ππ ππππππ a. Show that Marginal Revenue of this function is proportional to the price (let πΎ = ( 1 π ) 1 π β ). To simplify the equation. b. calculate the Marginal Revenue when πππ’πππ = …

## Lim x-> infinity (1-(e^x))/(1+(2e(^x)))

Lim x-> infinity (1-(e^x))/(1+(2e(^x))) EXPERT ANSWER To find the lt –> infnity {(1-e^x)/(1+2e^x)}, we transform e^x = y and so when x–>ifinity, y = e^x –>ifinity. Therefore, Lt x–> ifinity {(1-e^x)/(1+2e^x)} = Lty–>infinity (1-y)/(1+2y) Lt x–> ifinity {(1-e^x)/(1+2e^x)} = Lty–>infinity (1-y)/(1+2y). We divide both numerator and denominator by y on the right: Lt x–> ifinity …

## A restaurant would like to estimate the proportion of tips that exceedβ 18% of its dinner bills. Without any knowledge of the populationβ proportion, determine the sample size needed to construct a 98% confidence interval with a margin of error of no more than 8% to estimate the proportion. could you pleast work this out step by step by showing me what to insert into my calculator?

A restaurant would like to estimate the proportion of tips that exceedβ 18% of its dinner bills. Without any knowledge of the populationβ proportion, determine the sample size needed to construct a 98% confidence interval with a margin of error of no more than 8% to estimate the proportion. could you pleast work this out …

## In these exercises, make reasonable assumptions about the graph of the indicated function outside of the region depicted. For the function g graphed in the accompanying figure, find lim x right 0- g(x) lim x rightarrow 0+ g(x) lim x rightarrow 0 g(x) g(0).

EXPERT ANSWER a) When x = 0, we are talkin about the y-axis And when they ask us to find the limit as x —> 0(-), we are looking at the value of y when x is approaching 0 from the negative side. Notice that at x = 0, y = 3. Also, when x …