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Calculus
Find the first partial derivative "\\displaystyle{\\frac{\\partial z}{ \\partial x}}" of the function "z=x^2e^{-y}" at point (2,-1)
Calculus
Use cylindrical shells to find the volume of the solid that results when the red region is revolved about the y
y-axis. f(x)=x^2 ,a=1 ,b=4
Calculus
What is limit of (x,y) tends to (0,0) 1/sinxy?
Calculus
The graph of f(x) = ex curves upward in the interval from x = - 1 to x = 1 Interpreting f(x) = ex as the slopes of tangent lines and noting that the larger x is, the larger exis, explain why the graph curves upward. For larger values of x, the graph of f(x) = ex appears to shoot straight up with no curve. Using the tangent line, determine whether this is correct or just an optical illusion.
Calculus
A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached to a boat at the constant rate of 2 ft/s. Assume that the boat remains at water level. At what speed is the boat approaching the dock when it is 20 feet from the dock? 10 feet from the dock? Isn’t it surprising that the boat’s speed is not constant?
Calculus
A 10-foot ladder leans against the side of a building as in example 7.2. If the bottom of the ladder is pulled away from the wall at the rate of 3 ft/s and the ladder remains in contact with the wall, (a) find the rate at which the top of the ladder is dropping when the bottom is 6 feet from the wall.
(b) Find the rate at which the angle between the ladder and the horizontal is changing when the bottom of the ladder is 6 feet from the wall.
(b) Find the rate at which the angle between the ladder and the horizontal is changing when the bottom of the ladder is 6 feet from the wall.
Calculus
The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the square increasing when the area is 150 cm^2.
Calculus
Show that 𝑈(−𝑓, 𝑝) = −𝐿(𝑓, 𝑝) and 𝐿(−𝑓, 𝑝) = −𝑈(𝑓, 𝑝)
Calculus
∫ csc2
(2 − 3
(2 − 3
Calculus
Find the equation of the line with slope equal to 1 and normal to the
curve x
2 + 3xy + y
2 = 5 at P0(x0, y0) when x0 = 1.
curve x
2 + 3xy + y
2 = 5 at P0(x0, y0) when x0 = 1.
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#340153 on Dec 2023
#340153 on Dec 2023