In Exercises 13–18, calculate the derivative in two ways. First use the Product or Quotient Rule; then rewrite the function algebraically and directly calculate the derivative. f(x) = x²(3 +x=1)

Q: Find the derivative of the function y=(x−1)(x−2)(x−3) at x=0.

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Q: The components of v = 240i + 300j represent the respective number of gallons of regular and premium ...

A: Vector: The components of v = 240i + 300j represent the respective number of gallons of regular and ...

Q: Add or subtract terms if possible: 33√24 + 3√81.

A: To Determine: add or subtract terms if possible Given: we have an expression 3243+813 Explanation: w...

Q: Solve the equation. 814X = 27x+ 2

A: Given,           814x=27x+2

Q: Use common logarithms to evaluate log7 2506.

A: we have to use the common logarithm to evaluate log72506. the common logarithm is logarithm with bas...

Q: Use a system of linear equations with two variables and two equations to solve. 246 students enrolle...

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Q: Find the derivatives of the functions s = cos4 (1 - 2t)

A: Given: st=cos41-2t we know that ddxxn=nxn-1                                                  ..1ddxc...

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: To evaluate I=∫72xdx

Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write as...

Q: Two sides and an angle are given below. Determine whether the given information results in one trian...

A: Given: Two sides of triangle, a = 5, b = 6 the angle, A = 80

Q: Find f(3x) if f(x) = 9 – 4x2. f(3x) = = (Simplify your answer.)

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Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). When d...

A: Given,The position at  time t ≥ 0 of a particle moving along a coordinate line is s=10 cos(t +π/4).W...

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary const...

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Q: Graphing curves Graph the curves described by the following functions, indicating the positive orien...

A: Given: The function rt=t,2t, for 0≤t≤1, To sketch: The graph of given function.

Q: The median waiting time (in minutes) for people waiting for service in a convenience store is given ...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Find the indicated term a12 of the arithmetic sequence with first term, a1=-8, and common difference...

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Q: How close to - 3 do we have to take so that

A: Suppose for some x,                             1(x+3)4> 10,000  

Q: Write an equation for each parabola.

A: Solution:- The labelled figure of above question is given below.    

Q: Find the product. (x + 8)(x + 5)

A: Given : (x + 8)(x + 5)

Q: b) ſ e2x sin 3x dx

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Q: Which point P should he choose in order to minimize the average length of his trip?

A: According to the question, consider a point P at a distance p, above or below, in the fence as shown...

Q: 6. Write and evaluate the definite integral that represents the area of the surface generated by rev...

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Q: Define the term Intermediate Value Theorem for Continuous Functions?

A: Intermediate value theorem states that, If “f” be a continuous function over a closed interval [a, b...

Q: Evaluate the integral. Check your results by differentiation. (Use C for the constant of integration...

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Q: You are creating a dessert called a "S’more" as follows: • You start with a (cylindrical) marshmallo...

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Q: Perform the indicated operations: 1 /( xn - 1) - 1/ (xn + 1) - 1/ (x2n - 1) ?

A: Given,            1xn-1-1xn+1-1x2n-1

Q: Write the equation of a sine function that has the following characteristics. Amplitude: 2 Period: 6...

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Q: (sec² x)e² – (tan x)e" (e=)? Suppose that F(x) is an antiderivative of f(x) 1. What is F'(x)? 2. Fin...

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Q: Areas of triangles Find the area of the following triangles T. The vertices of T are A(0, 0, 0), B(3...

A: Solution;- The vertices of  Triangle is  A(0,0,0)B(3,0,1)C(1,1,0)

Q: The value V of a machine t years after it is purchased is inversely proportional to the square root ...

A: Given, The value V of a machine t years after it is purchased is inversely proportional to the squar...

Q: Parametric descriptions Write parametric equation for the following curve. Solutions are not unique....

A: Let (h,k) be the center and r be the radius of any circle, and the circle is generated counterclockw...

Q: Find a power series representation for the function of convergence. f(x) = 1/1+4x^2 and determine ...

A: Given : The function , f(x) = 11+4x2   To find : A power series representation for the function of c...

Q: Determine whether the equation is true or false: ln 0 = e. Where possible, show work to support your...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Calculating derivatives Find the derivative of the followingfunctions. y = sin x + 4ex

A: Given function:                              y=sinx+4ex   Taking derivative with respect to x :     ...

Q: Simplify the expression shown.

A: To simplify the expression ddt∫0t11+x2dx+∫11t11+x2dx

Q: solve the differential equation. dy/dx = √y cos2 √y

A: It is given that, dydx=ycos2yWe have to solve the differential equation.  

Q: Determine whether the graph of y = x3 is symmetric with respect to the y-axis, the x-axis, or the or...

A: Given: y=x3 for finding symmetry of given expression, we sketch the graph of given expression as bel...

Q: The larger circle in the figure is the graph of r = 1. Find the polar equation of the smaller circle...

A:                           From Pythagoras Theorem AB⇒r=r12          1=r12          r1=12 Let radius ...

Q: Use a graphing utility to sketch the intersecting graphs of the equations and show that they are ort...

A: Given : x 3 = 3 ( y − 1 ) x (3 y − 29) = 3   To determine :  Using a graphing utility to sketch the ...

Q: Find the areas of the triangles whose vertices are given A(-1, -1), B(3, 3), C(2, 1)

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Q: c) Sa* sin*x dx

A: To evaluate : The integral  ∫π43π4 sin4 x dx . 

Q: 4.5 please show me all steps

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Q: Find each limit.

A: Given: limx→∞sinxx We know that -1≤sinx≤1 Then, -1x≤sinxx≤1x