Find the point (a, b) on the graph of y = e^x where the value ab is as small as possible.

Q: The radius of a right circular cylinder is increasing at a rate of 4 inches per minute, and the…

A:

Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: 3.

A: Indefinite Integration

Q: ; Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Please refer to the image below.

Q: 1. у %3D х+/x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Let the volume of the rod be V Radius of the rod be R and length be L Given: L=20cm; R=3 cm…

Q: What is the rate of change of the area?

A:

Q: A fighter plane 2000 km away is spotted by a gunner in the ground. If it maintains its altitude at…

A: Pythagoras theorem: In a right angle triangle, Hypotenuse2=Base2+Perpendicular2 Differentiation…

Q: Use differentials to estimate the value. estimate =  exact value =

A:

Q: A woman 1.5 m tall walks directly away from a street light which is 6 m above the ground at a rate…

A:

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: To solve the following problem of finding the rate of change in height

Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

A:

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?

A: The rate of growth of a patch of moss is modeled by a complex function A't, where t is measured in…

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Rate of change

Q: A metallic ball with a diameter of 12 cm is covered with a layer of ice, so if the ice begins to…

A:

Q: 6. y%= arcsin a Va2-x2

A: Given: 6. y=xa2-x2-arcsinxa

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Let V is the volume of the pool. Water is pouring at the rate of 9 cubic feet per minute, means…

Q: A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The length…

A: Given:A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The…

Q: A rectangle has a length of 1 inches and a width of 12 inches whose sides are changing. The length…

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Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

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Q: use differentials to estimate the amount of metal in a cylindrical can that is 12cm high and 8cm in…

A:

Q: A rectangle has a length of 4 inches and a width of 12 inches whose sides are changing. The length…

A: Let x and y be the length and width of the rectangle at any time t respectively. Now according to…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.1 cm/min. At what is…

A: The diameter of the snowball is decreasing at a rate of 0.1 cm/min. So, the decreasing rate of…

Q: A point is moving along the graph of x3y2 = 200. When the point is at (2, 5), its x-coordinate is…

A: Given that a point is moving along the graph x3y2=200 and it's x-coordinate is changing at the rate…

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

Q: A 25,000 machiene depreciates linearly to 0 over a ten year period.What is the value of the machiene…

A: The Initial value of machine is 25000 and its depreciates linearly to 0 over a ten year period. We…

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: A right triangle has legs of 18 inches and 24 inches. The short leg is decreasing by 3 in/sec. The…

Q: Use differentials to approximate the change in the area of a square if the length of its side…

A: Area of a square with a side length of x cm is, Ax=x2 Here, x=5 cm & ∆x=5.32-5=0.32 cm Now…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.1 cm/min. At what is…

A:

Q: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

A: We construct a triangle as shown below.

Q: A rectangle has a length of 11 inches and a width of 10 inches whose sides are changing. The length…

A:

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

A:

Q: A rectangle has a length of 12 inches and a width of 6 inches whose sides are changing. The length…

A: The length of a rectangle is l=12 inThe width of a rectangle is w=6 inTo find the rate at width the…

Q: A rectangle has a length of 9 inches and a width of 10 inches whose sides are changing. The length…

A: Length of the rectangle, l =9 inches Width of the rectangle, w = 10 inches The length is increasing…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A:

Q: Calculate the derivative. y=3/log5x

A: Given function is

Q: A point moves along the curve y of 2 units per second. At what rate is x changing when = = 2x2 1 in…

A: According to the question, we have to find the rate of the x when x=-32, if the rate of change of y…

Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

Q: A cone shaped icicle has an initial radius of 10 inches and a height of 15 inches. Once the height…

A:

Q: A rectangle has a length of 7 inches and a width of 8 inches whose sides are changing. The length is…

A:

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 33 inches and 44 inches . The short leg is decreasing by 4…

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A:

Q: A rectangle has a length that is increasing at a rate of 16 mm per second with the width being held…

A:

Q: Mohamad Salah poured orange juices into a cylindrical red tank whose height = of its radius. If the…

A: We have to find rate of change of Radius.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.