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

Q: Find the rate of change of 1/x with respect to x when x=2

A: f(x)=1xrate of change of 1/x with respect to x isdf(x)dxdf(x)dx=-1x2

Q: What is the instantaneous rate of change of the graph of y = = cos x when x= 2n?

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Q: The length of a rectangle is increasing at the rate of 2 ft/sec. The width is decreasing at 5…

A:

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 4 inch(es) per…

A: Let r be the radius of the snowball at any time t. The radius r is decreasing at the rate of 4 in/hr…

Q: 1. Related Rates: Find when x dt dr

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Q: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

A:

Q: A right triangle has legs of 3 inches and 4 inches whose sides are changing. The short leg is…

A: dhdt=7 in/sec , dbdt = -10 in/sec

Q: 9. When a particular plate of metal is heated in an oven, its radius increases at the rate of…

A:

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

A: Explanation: Given that,  y=lnx   Concept Used: To find the rate of change we will find the…

Q: A spherical snowball is melting so that its diameter is decreasing at a rate of 0.4 cm/min. At what…

A:

Q: Find the rate of change. Volume of a cube with respect to its sides when s = 5

A: The volume of a cube with side s is V=s3 Differentiate with respect to s dVds=ddss3=3s2

Q: A bacteria decreases at a rate of 15% continuously when exposed to ultraviolent light. If a culture…

A:

Q: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How…

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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 triangle has an area that is increasing at a rate of 555 square feet per minute with the height…

A:

Q: 2. A tank with a shape of a cone is 20 feet deep and has a diameter of 10 feet at the top. Water is…

A: Given; Diameter = 10 feet  Height = 20 feet

Q: If I am blowing up a balloon at a rate of 3 cubic feet per minute, what is the rate of change of the…

A: Since, it is given that a person is blowing up a balloon at a rate of 3 cubic feet per minute, then…

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

A:

Q: A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the ground…

A: Given:A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the…

Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

A:

Q: A rectangle has a length of 11 inches and a width of 5 inches whose sides are changing. The length…

A: In the given rectangle  Width b = 5 inches Length l = 11 inches Length increasing rate dl/dt = 9…

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: 19. A spot light is on the ground 6 meters away from a wall and a 1.8-meter tall person is walking…

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: w many times between two points do we have an Instantaneous Rate Of change equalling Average ro

A: To determine the number of times the instantaneous rate of change equals to the average rate of…

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: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

A: Given that water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. And the…

Q: 3 of its radius. 4 Mohamad Salah poured orange juices into a cylindrical red tank whose height f the…

A: Topic:- application of derivatives

Q: 2. The radius and lateral area of a right circular cylinder change at the rates of 1 cm/s and -2…

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Q: The area of a rectangle remains 30 cm2. One side of the rectangle is expanding at a rate of 1 cm/s.…

A:

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

A:

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Given that rate of decay is proportional tp the current amount x.So,dxdt=kx,    where k is…

Q: A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 2…

A: Given Data: The initial population of bacteria is: P0=260 The population of bacteria after 2 hours…

Q: The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain…

A:

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

A: Solution:

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 rate of change of the ice circle's area towards the start of spring if the initial radius…

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: What is the instantaneous rate of change of y=y=−2x^2+2x at x=0 ?

A:

Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

A:

Q: The side of a square is increasing at the rate of 0.2 cm/sec . Find the rate of increase of the…

A: we know that the perimeter of the square is with side x is                        P=4x…

Q: The altitude of a triangle is increasing at a rate of 1 cmminwhile the area of the triangle is…

A: Givendhdt=1cm/mindAdt=2cm2/minA=100cm2h=10cm

Q: Air is being pumped into a spherical balloon such that its radius increases at a rate of .50 in/min.…

A: r= 3 in dr = 0.5 in/min

Q: A circle is inside a square.The radius of the circle is increasing at a rate of 3 meters per minute…

A: First, find the area outside the circle but inside the squareLet ‘s’ be the side of the square and…

Q: 1. When a circular plate of metal is heated in an oven its radius increases at a rate of 0.01…

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: 2. The volume and radius of a right circular cylinder change at the rates of 1 cm^3/s and -2 cm/s,…

A: Given : Radius = 2cm, height = 1 cm Rate of change of radius is 2 cm/s and rate of change of volume…

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

A:

Exponential Growth Model

The relation that represents an exponential function is: