20 inches

Q: Find the following derivative

A: Explanation of the solution is given below..

Q: True or false?

A:

Q: Derivatives from limits The following limits represent ƒ′(a)for some function ƒ and some real number...

A: limx→0ex-1x a). limx→0ex-1x=limx→0ex-e0x-0 Now comparing with limx→afx-fax-a, we get fx=ex & a=0

Q: The amount of caffeine in the bloodstream decreases by 24% every hour. A cup of coffee contains 98...

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

Q: Evaluate the iterated integral. '1 cos(s³) dt ds Jo Jo

A: Given- ∫01∫0s2coss3 dtds To evaluate- The iterated integral.

Q: Consider the function g(x): y = x² • V3- 2x. a) State the domain of the function. dy b) Determine dx...

A:

Q: 4. Find all points of discontinuity in the function below. For each point, tell me which sort of dis...

A: Given: fx=x2-2ifx<25x-8if2≤x≤7x-9x2-10x+9ifx>7

Q: Find an equation of the plane. The plane that passes through the point (−3, 3, 3) and contains the l...

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Q: Evaluate each of the following integrals if it converges. Say it diverges if that applies.

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Q: In a mountain range of Califormia, the percent of moisture that falls as snow rather than rain can b...

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Q: What happens to the equation x2 + y2 = r2 in a rotated x′y′-system?

A: Given- x2+y2=r2 To find- The transformed of the equation in x'y' plane. Concept Used- To find the tr...

Q: Topic. Equations of Conic Sections, Systems of Non-linear Equations Competencies: recognize the equa...

A: x2+3x-y+2=0   →1y-5x=1               →2   From equation (2), we get y=1+5x Now put y=1+5x in equatio...

Q: Use the ratio testor the root test to determine whether the series converges or diverges.

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Q: Graph: x2 + 4y2 + 10x + 24y + 45 = 0. Where are the foci located?

A: Given- x2+4y2+10x+24y+45=0 To find- Focii and draw the graph of the above equation. Concept Used- Th...

Q: The circumference of a circle is increasing at a rate of 2 meters per second. How fast is the radius...

A: Let P be the circumference of circle. Given: dP/dt = 2 m/sec To find the rate of change of radius

Q: Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, y)...

A: Note: where △f(x,y) = ∂f∂x,∂f∂y  

Q: Compute (a) lim rlnr (b) lim r100 200

A: Explanation of the solution is given below....

Q: The rectangular coordinates of a point are given. Plot the point. (−2, 3) Find two sets of polar coo...

A: x, y=-2, 3 The point on the graph is,

Q: Find an equation for the function f that has the given derivative and whose graph passes through the...

A: The function f that has the given derivative f'x=sec22x and passing through point π2,2. Now, f'x=sec...

Q: Use this theorem to find the curvature. r(t) = 7ti + 5sin(t)j + 5 cos(t) k

A: Consider the provided vector valued function, rt=7ti+5sintj+5costk Using the above theorem find the ...

Q: S cos³ x sinxdx

A:

Q: I really need help with this please.

A: Given a headlight reflector is in shape of parabola.  And headlight is in bowl shape.  The headlight...

Q: Find the general antiderivative of f(x)=x3+6x+3x4−2√xf(x)=x3+6x+3x4-2x    + C

A: The given function is  f(x)=x^3 +6x+3x4−2√x  To find the anti derivative we have to find integration...

Q: Using trig. substitution. Please detailed prodecure. Thank you!

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Q: 3V3 Let f(r) = sin (2r) so that f () = 2 0.6495 (a) Find linear function for the tangent line to y =...

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Q: I need help finding the slopes

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Q: Find the length of the curve over the given interval.

A: To find the length of curve

Q: need help with this question about volume and arc length

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want rem...

Q: Determine the qiwen and State the theoren

A: ∑n=1∞ 1n3n2+1 Apply comparison test let0≤an≤bn   if ∑n=1∞ bn converges then ∑n=1∞ an converges let b...

Q: Represent the function 4 In(10 – 1) as a power series (Maclaurin series) f(z) = >, n=0 CO C2 = CA = ...

A: Given function is 4 ln(10-x) find out the Maclaurin series of the given function  as fx=∑n=0∞cnxn fi...

Q: ou can find the temperature inside your refrigerator without putting a thermometer inside. Take a ca...

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Q: Explain how to find the partial fraction decomposition of a rational expression with a repeated line...

A: Explain how to find the partial fraction decomposition of a rational expression with a repeated line...

Q: y=2.2x+12      x= y=2x−6.1     x= y=5(x+5)−1 x=

A: 1. Given y = 2.2x + 12 y= 4x + 12 4x = y - 12 x = (y - 12)/4 Or   x = (y/4) - 3

Q: find the taylor power series representation for f(x)=cubed root of x centered at x=1

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Q: Use the graph to determine a. intervals on which the function is increasing, if any. b. intervals on...

A: Given: To find: a. Interval on which the function is increasing. b. Interval on which function is d...

Q: Determine how large the number a has to be so that     ∫a∞ 1/(x2+ 1) dx < 0.001

A: It is given that, ∫a∞1x2+1dx<0.001. Show the definition of an improper integral of type 1: (a) If...

Q: Consider the following. Зx + 2у + 62 3 36 Sketch a graph of the plane.

A: 3x+2y+6z=36 To find x-intercept, put y=0 & z=0, we get 3x+20+60=36⇒3x=36⇒x=12 To find y-intercep...

Q: A bacteria culture grovs with a constant relative growth rate. After 2 hours there are 600 bacteria ...

A: Given: A bacteria culture grows with constant relative growth rate. After 2 hours there are 600 bact...

Q: Topic: Equations of Conic Sections, Systems of Non-linear Equations   Competencies: recognize the eq...

A: 1. Given equation is 9x2+72x-64y2+128y+80=0. Given equation can be written as: 9x2+72x-64y2+128y+80=...

Q: y = log x where x = e Find the tangent line and normal line

A: Consider the following equation: y=logx                       ...... 1 Substitute x=e in the above e...

Q: A right circular cylinder is inscribed within a sphere, what is the least possible volume of the cyl...

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Q: Use logarithmic differentiation to find the derivative of the function

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.