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Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).

A: We first write the given function in the form of the definition of the derivative.

Q: Approximate the area of the shaded region using the Trapezoidal Rule and Simpson's Rule with n = 4. ...

A: Given information:The value of n is 4.

Q: p(q)=2q2-4q+5; q=2 (a) Find the derivative, by using the definition. (b) Find the instantaneous rate...

A: Part (a)The derivative of p(q) at any point q, by using the definition, will be given by the express...

Q: Is y=ex −5x−8 a solution to the initial value problem shown below? y′−5x=3+y y(0)=−7

A: The given differential equation is y=ex −5x−8.The solution of the deferential equation is given as, ...

Q: find the exact length of the curve of the equation in the picture below make sure to show all work

A: The given curve equation is,

Q: Help in #1 please.

A: Given information:The parametric equation is

Q: The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have...

A: Here, we are given that for a real number 1< p < 2 , the graphs of y=px and y=x have exactly o...

Q: If y x4x+3, then 2ix+3ix3 2i 3ix3 O (4x+1)/4x+3 2Ax+3 2x vi3Ar3

A: The function is given by,

Q: Need help with D, E, and F. Anser A- h= 17.92/(pi)r^2 Answer B-S(r)= 35.84/r + (pi)r^2 Answer C- S'...

A: Given information:The surafce area of the baking powder is shown below:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by x ...

A: We are given equations as

Q: 2.5 Continuity 3. We would like to find a value of k to make the piecewise function f(x) continuous ...

A: 3)Answer: a) If I was to graph f(x) then the left part of 3 is changed when k is changed. As the k i...

Q: The heat flow vector field for conducting objects is F=−k∇T, where T(x,y,z) is the temperature in t...

A: Assume k = 1.Then the vector field becomes, F = −∇T.Find ∇T as follows.

Q: Find the area of the region that lies inside both curves. r = 9 + cos(θ), r = 9 − cos(θ)

A: To calculate the area of the given region (by integration) described by polar coordinates

Q: You must get from a point P on the straight shore of a lake to a stranded swimmer who is 60 meters f...

A: Let, "u" be the velocity at which you can swim and "v" be the velocity at which you can run.u = 2 m ...

Q: Consider the following velocity function. Complete the sentence: The same distance could have been t...

A: The given velocity function is,

Q: How can I get the result? Which is the result?

A: The given function is,

Q: 1. Estimate the volume of the solid that lies below the surface z = xy and above the following recta...

A: You have asked two unreleated questions in the same post. Further your first question has multiple s...

Q: The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a tel...

A: Given information:Tyhe given function is cosh(x).

Q: Help please.

A: The given function is (tan-1x)2.

Q: A hot-air balloon is 190 ftabove the ground when a motorcycle (traveling in a straight line on a h...

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the bal...

Q: Evaluate the integral. Integral from nothing to nothing hyperbolic cotangent StartFraction x Over ...

A: Refer to the integral,Rewrite the hyperbolic cotangent as,

Q: What is the particular solution for y′=5ex −6x3 +4x such that y(0)=−8? Do not include "y=" in your a...

A: The given differential equation is, y′=5ex −6x3 +4x.

Q: Hello, How is tan^-1 (tan (6pi/7)=-pi/7 possible? I don't know how it should be a negative or to use...

A: First consider:

Q: All boxes with a square base, an open top, and a volume of 210 ft cubed have a surface area given by...

A: Approach:As a first step we will differentiate the given function and equate it to zero to find all ...

Q: Use spherical coordinates to find the volume of the region outside the cone phi= pi/4 and outside th...

A: To calculate the volume by using the spherical coordinates of the region outside the cone φ=π/4 and ...

Q: Help with #7

A: Given information:The equation of the curve is

Q: Evaluate the integral in cylindrical coordinates. Please see attached image.

A: To calculate the value of the integral in cylindrical coordinates which is shown below,

Q: Help w/ #6

A: The curve is given by ti+t2j+t3k.The formula to calculate the curvature of the curve is given by,

Q: please explain how to solve this

A: (a)We are given graphand we can locate upper and lower curves on different regions

Q: Determine the radius and interval of convergence of the following power series. к?(- 5)2к k! The rad...

A: Given,

Q: The rectangular coordinates of a point are given. Find the polar coordinates (r,0) of this point wit...

A: The given rectangular coordinates of a point is,

Q: How can I get the result? Which is the result?

A: we are given a graph and locate direction

Q: Determine the radius of convergence of the following power series. Then test the endpoints to determ...

A: The power series is given as

Q: Differentiate y = (s - sqrt(s) ) / s^2 I don't understand what happens on step 3 of the screenshot...

A: Here use quotient rule of differentiation which is,

Q: Find the function F that satisfies the following differential equations and initial conditions F'''(...

A: We are given second derivative as

Q: How can I get the result? Which is the result?

A: The given function is given by

Q: Help me please..

A: The Taylor series for cosx at x=0.

Q: Does the series converge absolutely, converge conditionally, or diverge?

A: The given series is

Q: Question 2 Pratice

A: Part A

Q: Find the producers' surplus at a price level of p $51 for the price-supply equation below. S(x) 5+0....

A: Given price-supply equation is,

Q: Find the volume of the solid generated by revolving the region bounded by the given line and curve a...

A: The given curve is,

Q: find the average rate of change for each function over the given interval y=x2+2x between x=1 and ...

A: The average rate of change of f(x) on the interval [a,b] is (f(b)-f(a))/(b-a). By substituting the v...

Q: If f(x) 3x-2then f(x) = x 2x+ 2x5/3 2x 2x-1 12 1+5x8/3 3x2 2x-53-3x-3/2 x2 none of the above

A: The given function is,

Q: Do the domain of the following function:

A: Consider the provided function.

Q: Help with #8

A: Let's understand the formula for calculation of curvature.For a function, y(x) the curvature is give...

Q: Help with #9

A: For a given curve r(t), the tangential component aT and the normal component aN are given by express...

Q: (3x2+5)8x-92 fy(1x4 + x2 logarithmic differentiation gives y (32+5)(8r-92 1x44+x2 16 2x 3x2+5 6-x9 6...

A: We have to find derivative using lograthmic differentiation .Question is given below:

Q: Water drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the...

A: By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r...

Q: The function f in the figure satisfies the lim f(x)=3 as x -> 2. Determine the largest value of ...

A: (A) We find the range of f(x) using |f(x)-3|<1.

Q: Suppose that the demand for a product is given by p= 1/2ln (5000-q/q+1) where p is in hundreds of d...

A: The elasticity of demand when the quantity demanded (q) is 2 and the price (p) is 3.71 hundreds of d...