Calculus Answers

Use implicit differentiation to obtain dy over dx

Cosx +sinx=xsquared+ysquared

Use implicit differenciation to obtain dy over dx

X over y+1 = xsquared+3y

Find the slope of the tangent line at the incident point

3e to the power x = xy+xsquared+ysquared at (0,1)

Write an equation of the tangent line

Use the technique of differentiation to find dy over dx

Y=(xcube+7xsquared-8) (2x to the power -3 + x to the power -4)

Evaluate the limits

Lim

X to 2

of

Xcube -8 over x-2

Let f(x)=x/3xsquared+1 and g(x)=square root of 1-x

Find

1. f+g

2. F-g

3. F/g

4. F of g

5. G of f

6. State the domain of g of f

Write a formula for the function g(x) that results when the graph of f(x)=x²     is horizontally stretched by a factor of 3, then shifted to the left 4 units, and then shifted down 3 units . Sketch the graph of f(x)  fas well as the graph of the new transformed function g(x)   

g(x)=? 

Consider the equations 5y²=16x and y²=8x-24. What is the pointbof intersection of the given curves on the first quadrant?⁼

The golf ball manufacturer has developed a profit model that depends on the number x of golf balls 

sold per month(measured in thousands),and the number of hours per month of advertising y, according 

to the function

𝑧 = 𝑓(𝑥, 𝑦) = 48𝑥 + 96𝑦 − 𝑥

2 − 2𝑥𝑦 − 9𝑦

2

,

Where z is measured in thousands of dollars .The budgetary constraint function relating the cost of the 

production of thousands golf balls and advertising units is given by 

20𝑥 + 4𝑦 = 216,

Find the values of x and y that maximize profit, and find the maximum profit

The golf ball manufacturer has developed a profit model that depends on the number x of golf balls 

sold per month(measured in thousands),and the number of hours per month of advertising y, according 

to the function

𝑧 = 𝑓(𝑥, 𝑦) = 48𝑥 + 96𝑦 − 𝑥

2 − 2𝑥𝑦 − 9𝑦

2

,

Where z is measured in thousands of dollars .The budgetary constraint function relating the cost of the 

production of thousands golf balls and advertising units is given by 

20𝑥 + 4𝑦 = 216,

Find the values of x and y that maximize profit, and find the maximum profit