The function f (x) = −0.015t3 + 1.05t gives the alcohol level of an average person’s bloodstream t hours after drinking 8 oz of 100-proof whisky. Find the rate of change of the alcohol level with respect to time when t = 2 hours.

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a grap...

A: Given: f(x)=5 x3-2-1 To determine: Slope of the given function at point -2, -12    

Q: Use properties of logarithms to expand the logarithmic expression logb x3 as much as possible. Where...

A: Given logarithm expression is logbx3. Properties of logarithm are: (1)logam=mloga (2)logab=logbloga ...

Q: Consider the equation below. (If an answer does not exist, enter DNE.) r(x) = x³ – 3x² – 9x + 3 (a) ...

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Q: Evaluate the integral.   ∫ 0 t ex Sin(t - s) ds

A: Consider the provided integral, ∫0texsint-sds Find the value of the integral. ∫0texsint-sds=ex·∫0tsi...

Q: Find dy/dx.  Y3 + (y+2)2 - 1 - x2 = x

A: Expand the left hand side expression and isolate the variables x and y. y3+y+22-1-x2=xy3+y2+4y+4-1-x...

Q: tell in what direction and by what factor the graphs ofthe given functions are to be stretched or co...

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

Q: 2) Find the volume of the figure below. It is a cylinder surmounted by a cone. 17 m 12 m 6 m

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Q: If f(x) = V4+4x, find f (4), using the definition of derivative. f' (4) is the limit as x → of the e...

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Q: 7. Use a double integral to find the volume under the surface z = xx² +y and over the rectangle R = ...

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Q: d²y then dx² cos x 2 dy Show that if y -+y = 0 x dx %3D

A: Given: y=cosxx To show: d2ydx2+2xdydx+y=0 Differentiate y with respect to x using the quotient rule ...

Q: Find both first partial derivatives. g(x, y) = ln√x2 + y2

A: Given function is gx,y=lnx2+y2 Partial derivative of function is derivative of function with one var...

Q: Find the given definite and indefinite integrals. Some of them will require substitution, integratio...

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Q: Use the given information to write the equation of the ellipse in standard form. Endpoints of minor ...

A: Given: Endpoints of minor axis :(1,8) and (1,0) Foci : (-2,4) and (4,4). Here, the y coordinates of ...

Q: 3 Let f(x) = ー1 Find f-1(x) and (ff)(x). Explain in detail all the steps.

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Q: If f(x)=4sin(x)+3x^x, find f'(3).

A: f(x)=4sin(x)+3xxnow differentiating both side with respect to xf'(x)=4cos(x)+3x.(xx-1)  

Q: Determine an appropriate viewing rectangle for each function, and use it to draw the graph. f(x) = 3...

A: fx=3sin120x Comparing with fx=asinbx, we get a=3 & b=120. Therefore, Amplitude=a=3Period=2πb=2π1...

Q: Some of the curves corresponding to different values of C in the general solution of the differentia...

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Q: Use point plotting to graph the plane curve described by the given parametric equation x = √t, y = t...

A: Given: x=t , y=t-1 To determine: Graph of given parametric equations.

Q: Solving equations of motion Given an acceleration vector, initialvelocity ⟨u0, v0⟩, and initial posi...

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Q: Find the limit of the sequence or determine that the limit does not exist. In(n + 7) an = n1/n 1 doe...

A: Given that an=lnn+7n1n. This implies that, an=lnn+7n1nlnan=lnlnn+7n1nlnan=lnlnn+7-lnn1nlnan=lnlnn+7-...

Q: A construction worker pulls a five-meter plank up the side of a building under construction by means...

A: Consider the equation

Q: When an angle’s measure is given in terms of π, I know that it’s measured using radians.Determine wh...

A: we know that, when a angle is measured in terms of π then it measured in radian

Q: Find the derivative of function (x+2)² (x – 1)3* f(x) -

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Q: 6. Find the values of c such that g(x) is continuous everywhere. fx² + c², 15c – x, x< 2 g(x) = x22 ...

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Q: Use L’Hôpital’s rule to find the following limit: lim x—&gt; infinity (ln5x - ln(x+6))

A: Answer is 0 Explanation is given below...

Q: The figure shows the graphs of y = 5x - x* and y = 4. Use the graphs to do the following. (a) Find t...

A: Given:             

Q: Need help for a and b please

A: f'(x)=-2x(x-3)2 We need to integrate the above function.f(x)=∫-2x(x-3)2dxf'(x)=-2x(x2-6x+9)       =-...

Q: A car was valued at $45,000 in the year 1990. The value depreciated to $12,000 by the year 2000. Use...

A: Given that: P = $45000 S = $12000 t = 2000 -1990 = 10 years   Use the compound interest formula, S=P...

Q: Preliminary steps The following integrals require a preliminary step such as a change of variables b...

A: ∫dyya-y=∫dyy·ya-y Now put  y=t⇒12y=dtdy⇒dyy=2 dt Therefore, ∫dyy·ya-y=∫2ta-tdt    →1

Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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Q: dx 2x

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Q: Describe with a sketch the sets of points 1x, y, z2 satisfying the following equations. y - z = 0

A: First sketch the graph of the function y-z=0 as shown below.

Q: please help

A: Given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectan...

Q: 1. Label all the critical points. 2. Label all regions where f'(x) < 0. 3. Sketch f'(x). Upload a si...

A: Given, Graph of f(x) is shown as:

Q: Use L’Hôpital’s Rule to evaluate the limit.

A: Given that: limn→∞ 1000 1+0.09nn .

Q: Find a linearization at a suitably chosen integer near a at which the given function and its derivat...

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a

Q: Consider the sequence whose nth term is an = 3 . 5n.Find a2/a1, a3/a2, a4/a3, and a5/a4. What do you...

A: Given: The sequence whose nth term is an=3×5n. To find: a2a1, a3a2,a4a3,a5a4.  

Q: 8. If lim f(x) = 9 which of the following must be true? I. f is continuous at x = 4. II. F(4) = 9. I...

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Q: Use a graphing device to graph the following functions. From the graph, determine whether the functi...

A: Consider the equation

Q: find the center, principal axis, the vertices, the endpoints of the minor axis, the length of the ma...

A: We have given equation x2+4y2=46.

Q: Determine if the series converges absolutely. converges, or diverges. 5n + 6 E (-1) In 5n +5 n=1 Div...

A: The correct option is the last option. Use the alternating series test to determine the characterist...

Q: Given f(x) = 2x - 3 and g(x) = 2x2 - x + 5, find each of the following: a. ( f ∘ g) (x) b. (g ∘ f ) ...

A: Given fx=2x-3 and gx=2x2-x+5 (a). We have to find fogx fogx=fgx=f2x2-x+5=22x2-x+5-3=4x2-2x+10-3=4x2-...

Q: What is the derivative of y if y = x2 + 5x + 15 evaluated at x = 2?Round you answer to three decimal...

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Q: Solve the rational inequality and graph the solution set on a real number line. Express the solution...

A: Given inequality is -x+2x-4≥0 We know that denominator can't be zero. Therefore, x-4≠0⇒x≠4 Finding c...

Q: A cone is constructed by cutting a sector from a circular sheet of metal with radius 29. The cut she...

A: Given A cone is constructed by cutting a sector from a circular sheet of metal with radius 29. The c...

Q: Evaluate the limit

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Q: Clearly state the quantity of the three sides in the right triangle you are going to use, and mark ...

A: Consider the given integral: ∫116-x232dx Let, x=4sinθHence,dx=4cosθdθ Therefore, integral becomes: ∫...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.