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Calculus
Find the value of 𝜕z/𝜕x and 𝜕z/𝜕y at the point (1,1,1) for the surface xy +z3x−2yz = 0 by differentiating implicitly.
Calculus
5. Find all the first and second partial derivatives of f(x,y)=x^(2) y + cos(xy) + tan(x/y).
Calculus
Prove that the following limit does not exist:
lim(x,y)->(1,1) (xy^(2)-1)/(y-1)
lim(x,y)->(1,1) (xy^(2)-1)/(y-1)
Calculus
3. Evaluate the limit
lim(x,y)->(2,2) (x-y)/(x^4-y^4)
lim(x,y)->(2,2) (x-y)/(x^4-y^4)
Calculus
For the function (2y+x)/(x-y-3)
write out an equation for a level curve for which f(x,y) = C. Your final equation should be of the form y = f(x,C). What is the level curve that goes through the point (1,2)?
write out an equation for a level curve for which f(x,y) = C. Your final equation should be of the form y = f(x,C). What is the level curve that goes through the point (1,2)?
Calculus
A cable hangs in a parabolic arc between two columns 100 feet apart. The columns are 40 feet high and the lowest point on the suspended cable is 10 feet above the ground.
a. Find the equation of the arc if the vertex is the lowest point of the cable.
b. Find the height of the cable from the ground at a point 30 feet from the lowest point of the cable.
a. Find the equation of the arc if the vertex is the lowest point of the cable.
b. Find the height of the cable from the ground at a point 30 feet from the lowest point of the cable.
Calculus
1. For the function f(x,y) = (25 − x^2 − y^2)^(−1/2), please sketch the level curves of the function, and then list the domain and the range of the function, write down a curve that represents the boundary, and state whether the domain is an open or closed region.
Calculus
y=5x^3+0x^2+x+7
Choose one integer from the following set: -5 ≤ x ≤ 5. State the integer you chose.
When using long division, what binomial would you divide by to determine if your chosen integer from part b is a zero for your polynomial?
Do the long division you just described in part c.
Write the answer to the long division problem in the form .
Is your integer from part b a zero of your polynomial? How you can tell from the long division work.
Choose one integer from the following set: -5 ≤ x ≤ 5. State the integer you chose.
When using long division, what binomial would you divide by to determine if your chosen integer from part b is a zero for your polynomial?
Do the long division you just described in part c.
Write the answer to the long division problem in the form .
Is your integer from part b a zero of your polynomial? How you can tell from the long division work.
Calculus
- y=5x^3+0x^2+x+7 & y=5x^4+0x^2+1
- Choose one integer from the following set: -5 ≤ x ≤ 5. State the integer you chose.
- When using long division, what binomial would you divide by to determine if your chosen integer from part b is a zero for your polynomial?
- Do the long division you just described in part c.
- Write the answer to the long division problem in the form .
- Is your integer from part b a zero of your polynomial? How you can tell from the long division work.
Calculus
Integrate sec^xlog(sinx)dx
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#340153 on Dec 2023
#340153 on Dec 2023