In Exercises 16–19, find the derivatives of the functions. Assume a, b, and c are constants.

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Q: Calculus Question

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Q: Calculus Question

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Q: . Lenny has 5 friends in his neighborhood. In how many ways can he choose 3 to help him move furnitu...

A: Lennh has friends = 5 Number of friend to be chosen = 3

Q: Use the quadratic function f(x) = 4x2 - 16x + 1000.Determine, without graphing, whether the function...

A: Given quadratic equation - f(x) = 4x2-16x+1000Here we can see that, there is no square root constrai...

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

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Q: Component Form of Vectors Express the vector with initial point P and terminal point Q in component ...

A: 9The given vector in component form,  The component of vector in x-direction is ax. Magnitude of ax ...

Q: Find (a) (f + g)(x), (b) (f - g)(x), (c) (f . g)(x), (d) (l)/(g)(x). What is the domain of (d)? f(x)...

A: The given functions are fx=3x-6 and g(x)=3-x. (a) Compute f+gx: f+gx=fx+gx=3x-6+3-x=2x-3 (b) Compute...

Q: Does (x - 3)2 + (y - 5)2 = -25 represent the equation of a circle? What sort of set is the graph of ...

A: x-32+y-52=-25 This equation does not holds true for any real values of x and y, because the sum of a...

Q: Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x...

A: fx=x,  gx=x+1 Now the graph is,

Q: 7. A differential equation is an equation which contains at least one derivative on it. *

A: A differential equation contains 

Q: An equivalent expression for(3x + 2/x - 5)with a denominator of (3x + 4)(x - 5) can be obtained by m...

A: 3x+2x-5 Here the denominator is x-5. Now to get a denominator of 3x+4x-5, we must multiply by 3x+4. ...

Q: A reservoir has the shape of a right-circular cone with its vertex down. The altitudeis 10 m, and th...

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Q: In Exercises 5-24, compute the derivative.

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Q: You need a total of 50 pounds of two commodities costing $1.25 and $2.75 per pound. (a) Verify that ...

A: [ Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for ...

Q: Plot the point (-2, 5π/4) in polar coordinates and find its rectangular coordinates.

A: Given: The point -2, 5π4  To plot: The given point in polar coordinates and find its rectangular for...

Q: Evaluate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or in...

A: the given expression is: limx→8x3-64xx-8  

Q: A rectangle is to be inscribed in a semicircle of radius 2. What is the largest area the rectangle c...

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Q: Evaluate 3 (9x² – 2x + 1)dx 1

A: Given:∫13 9x2-2x+1 dxIntegrating formula:∫xn dx=xn+1+C

Q: Question-based on, "write in standard form"... please note both are separate*.   Any help would be a...

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Q: Chain Rule with one independent variable Use Theorem 15.7 to find the following derivatives. dz/dt, ...

A: Given: z=x2y-x y3 , x=t2 & y=t-2 To determine: dzdt

Q: Evaluate the integral by changing to cylindrical coordinates. 16-1 c16-r² -y? Vx2 + y? dz dy dx = 64...

A: Given: The given integral is, ∫-44∫016-x2∫016-x2-y2x2+y2dzdydx. The objective is to evaluate the giv...

Q: 15.2 8

A: Given force is, Fx,y=xi+8yj Path traveled, x=t, y=t3 from (0, 0), (6, 216).

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the s...

A: Consider the provided curve, y=x2,y=9,x=0 Find the volume of the solid obtained by rotating the regi...

Q: dz = +1 Select one: tan a. +C +C I + tan -z+C tan 'z+ C it b. d.

A: Given: ∫x4x2+1 dx To find: Value of the integral.

Q: Determine whether the series converges, and if so find its sum.

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Q: IF lim h>0 f(5h•1)-F(1) - 10 lim FIND 670 F(h+1)-f(1)

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Q: %3D Funetion 3. В) Considen evenywhere i's domain - il Prove that L is differentiable ii) Find formu...

A: (i) The derivative of the given function Lx=lnx in its domain x>0,  is given by the limit, L'x=li...

Q: Solve the critical points of f(x)=2x²(x-3) ² for x only.

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Q: The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bon...

A: given half life is 5750 years  using formula N = Noe-λt where N = mass remaining after time t No = i...

Q: Find all the values of x such that the given series would converge.

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Q: Use spherical coordinates. Evaluate /| y² dV, where E is the solid hemisphere x2 + y² + z² s 9, y 2 ...

A: first convert x,y,z coordinates into hemispherical coordinates than perform integral  detailed solut...

Q: Solve the two mcqs below

A: Given  The set of sign chart of first and second derivative of function f .    

Q: Martha has $20. She is deciding whether to take the following bet: A coin will be flipped, and if th...

A: Given, money with Martha=$20

Q: dw A) Give the general solution of 4w dx

A: Given: dwdx+4wx=x3 ...........1 Now for general solution: Let  μx=e∫4xdxμx=e4logxμx=x4 Multiply both...

Q: Solve this...................

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Q: Calculus Question

A: ∫08f(x)dx To find the area of the integral x=0 to 8 , break the interval and find the area ∫08f(x)dx...

Q: In 2012, the population of a city was 5.91 million. The exponential growth rate was 1.56% per year. ...

A: Given: In 2012, the population of city was 5.91 million and the exponential growth rate was 1.56% pe...

Q: Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the...

A: Surd zeros are always in pairs. That is a+b is zero then a-b is also a zero of the polynomial.  Ther...

Q: Demand function Sales records indicate that if Blu-ray players are priced at $250, then a large stor...

A: The given coordinates are Pa,fa=250,12 and Qx,fx=200,15. From the difference quotient we get m=fx-fa...

Q: Consider the quadratic function below and (a) find the vertex; (b) find the axis of symmetry; (c) de...

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