Calculus Question

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A: Let N be the population (number) of bacteria at any time t. Hence, the corresponding equation f or t...

Q: I need help with Calculus HW. I need to differentiate problem #25 on page 188, Section 3.2, of the J...

A: Given, 

Q: (a) Find the differential dy. y = rad(15+x2) (b) Evaluate dy for the given values of x and dx. x = 1...

A: a). Given, 

Q: Describe a function g(x) in terms of f(x) if the graph of gg is obtained by vertically stretching f ...

A: Function obtained by stretching f by a factor of 4 will be 4f(x)Function obtained by shifting the fu...

Q: The function p gives the number of miles from an airport that a plane has flown after t hours. (a) W...

A: Given,           The function p gives the number of miles from an airport that a plane has flown aft...

Q: Please see the attached problem. Thanks!

A: To determine the volume of shell.

Q: Find the linearization L(x) of the function at a. f(x) = rad(x),    a = 25

A: Given, 

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

Q: a. Use the definition mtan = lim I(x) - f(a) to find the slope of the line tangent to the graph of f...

A: (a) to determine the slope of the tangent at the point P to the given curve y=f(x), using the limit ...

Q: Give the derivative formula for the function. j(x) 4 In x e5 = j(x)

A: The function is given by,

Q: 95. Tangent lines Find the equation of the line tangent to y = eat 1 In 3. 2 Comnition containino si...

A: It is given that, y = e2x and x = ln 3/2.Differentiate y with respect to x.

Q: For each of the following, find an explicit formula for an example of a function satisfying the giv...

A: Beginning with the definition,An absolute maximum point is a point where the function obtains its gr...

Q: Differential Equation Show a comple te solution 11 2X 2-y-ay e t2

A: Firstly, we find complementary function by solving auxillary equation

Q: The trough in the figure below has width w=4, lengthL=20 ft and height h=6. If the trough is full of...

A: The base, height and length are 4ft, 6ft and 20ft, respectively.Then the thickness of the triangle i...

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A: In order to find symmetries graphically, Visualize folding the graph along y axis. If the graph on e...

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A: Given,

Q: A woman invests a total of $20,000 in two accounts, one paying 4% and the other paying 7% simple int...

A: The simple interest I for the principle P with interest rate R for T years is given by

Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 15 and f'(2) = 4 (Use symbolic notati...

A: To write down the equation of the tangent using the given data

Q: For the following problem, use the position function -16t^2 + v0t+ s0 for free following objects. A ...

A: Calculation:Let s(t) = −16t2 + v0t + s0.At the height of 1296ft, the v0 = 0 and s0 = 1296.Thus, s(t)...

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A: Given triangle is right angle triangle (ABC) given by below figure

Q: Find an equation of the tangent line to the curve at the given point    y= xe^-x^2 , (0,0)

A: Given,

Q: Find the asympototes of f(x)= x4-2/x3+1

A:  f(x)= x4-2/x3+1 We can find the vertical asymptotes by finding the values that make the function un...

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A: Given

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A: To represent the given function graphically and identify its domain and range

Q: The population of a certain species of bird is limited by the type of habitat required for nesting. ...

A: Given:‘t’ is measured in the year.Here, the equation of the logistic growth model:

Q: A.Find the linear approximation of the function  f(x) = Radical(4-x)at a = 0. B.Use L(x) to approxim...

A: Given,

Q: Evaluate the piecewise defined function at the indicated values.

A: We are given the function to be

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A: Given,           Amplitude = 12 in.           Period = 1 seconds.           Since, d at t = 0 is 0 i...

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A: In y=a*sin(bx)Amplitude= |a|And period = 2pi/b

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A: Given,

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A: The expression is given by

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A: Compound interest formula:

Q: For the function f(x)=4x2+2x, evaluate and simplify.   f(x+h)−f(x)/h=

A: Given function is:We need to evaluate and then simplify it.

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A: For the function y=Asin(Bx+C)+DAmplitude =magnitude of APeriod=2pi/BPhase shift=-C/B

Q: Find the inverse function of f(x)=12+3√x.

A: Given,

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A: a)Find the value of sin2 θ

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A: The given function is a rational function, the vertical asymptotes are the undefined points also kno...

Q: i am having trouble with part c i have one more chance to get it correct

A: Part (c)To find the average rate of change of profit when the ticket price rises from $350 to $400.

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A: Recall the given rules.

Q: solve-  (sin π/4 cos π/6− sin π/6 cos π/4) ^2

A: Given, 

Q: Evaluate the piecewise defined function at the indicated values.

A:

Q: Evaluate the piecewise defined function at the indicated values. x2 f(x) if x -1 + 4x if -1 < x s 1 ...

A: Substitute the value x=-4 in f(x)=x^2+4x.

Q: Find the derivative of the function.(x2 + 9)(x3 + 6)/ x2 + 3

A: Consider the function

Q: Find the second derivative. f(x) = 5e−x − 3e−5x f ''(x) =

A: Recall the following facts.

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A: Calculation:Solve the given inequality as follows.

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A: The equation is given by,

Q: Write the formula for the derivative of the function k(x)2x2+ 14x + 1 (Hint: Rewrite as three separa...

A: First we simplify k(x) and write as three separate terms.

Q: The function e(m) represents the elevation above sea level in feet of the Mississippi river a distan...

A: Given function e(m) represents the elevation above sea level in feet of river at m miles from the so...

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A: Given,