(x - 1 if x s 1 if x>1 f(x) =

Q: Let s(t) = 6t3 + 9t² – 216t be the equation of motion for a particle. Find a function for the veloci...

A: Velocity is the rate of change of position wrt time. v(t)=ddts(t) ----------------------------------...

Q: A coffee pot in the form of a circular cylinder of radius 5 in. is being filled with water flowing a...

A: Let r and h be the radius and height of the circular cylinder. Given that, A coffee pot in the form ...

Q: Number 2

A: Given data: 2(a) The given inequality of the function is x+lnx ≤  xlnx+1.   The given expression can...

Q: Number 33

A: Consider the given information.   Le the demand of the house is represented by x and the price is by...

Q: 49. E ) converges, so the series converges. n=0

A: Given: ∑n=0∞1011n first we expand given sum for n=1,2,3,4....... so, S=1011+10112+10113+10114+.........

Q: A retail chain will buy 1100   cordless phones if the price is ​$10   each and 700   if the price is...

A:

Q: Find the solution of the initial value problem (28) y′′+5y′+6y=0,y(0)=2,y′(0)=3.

A:

Q: 29. Determinant of an Inverse Prove for invertible matrix A that

A: To prove: A-1=1A  

Q: Let h(x)=−2x2+x+4x2+4x−1, what is h′(−5)?

A: Consider the following function: hx=-2x2+x+4x2+4x-1=2x2+5x-1 Differentiate the above function with r...

Q: Use the Chain Rule to find the indicated partial derivatives. z = x4 + xy3,    x = uv3 + w4,    y =...

A: Definition used-  Chain rule of derivative - The derivative of a composite function is the product o...

Q: Evaluate the improper integral or state that it is divergent. dt 2- 4t

A:

Q: find the general solution of x(y+1) dx -x 2 dy=0

A:

Q: Number 1

A:

Q: I need help solving this problem using optimization. I have drawn the picture and I set the two angl...

A: Let angle c be the difference between the angles a and b.Find cotangent a and b from the figure. cot...

Q: Suppose θ(t) measures the minimum angle between a clock’s minute and hour hands in radians. Find, θ'...

A: Given that:  θ (t) measures the minimum angle between a clock’s minute and hour hands in radians. An...

Q: question-based on, "find the maximum value".   Incorrect answer: (3/2,29/4)   I have tried it but un...

A: Using the Maxima and minima then maximum value is 29/4.

Q: Find the derivative of the function f by using the rules of differentiation.

A:

Q: Which Integration formula should I use?

A:

Q: Solve the system: 7z - 3 = 2(x - 3y), 5y + 3z - 7 = 4x and 4 + 5z = 3(2x - y)

A: To solve the following system of equations: 7z-3=2(x-3y)5y+3z-7=4x4+5z=3(2x-y)

Q: What are the coordinates of the point of intersection of y=2x-5 and y=5-3x

A:

Q: Convert the polar equation r = -10 cos θ to a rectangular equation. Then use your knowledge of the r...

A: r=-10cosθ Now the rectangular equation is, r=-10·xr       ∵x=rcosθ⇒r2=-10x⇒x2+y2=-10x    ∵r=x2+y2⇒x2...

Q: Evaluate the following integral.  r3 lnr dr from upper bound: 3, lower bound: 1

A:

Q: Just the marginal profit function

A: The profit function is given by,  P(x)=-.000001x3+.005x2-290x-80000.  

Q: f(x) = -2x X- 13 - 2x

A:

Q: The curve given by x =sqrt(a2+y2) where -a ≤ y ≤ a; is rotated about the y –axis. Find the resulting...

A: Given curve is x=a2+y2  where -a≤y≤a Differentiate the given curve with respect to y, dxdy=ya2+y2 Af...

Q: Need help with ones circled. Thanks!

A: (11) The maximum number of beats in one minute: Hx=208-0.7x   The term x is the age of a healthy adu...

Q: The graph of ƒ is shown. Let A(x) be two area functionsfor ƒ. Evaluate F(8)

A: & Fx=∫4xft dt

Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2 ...

A: Given data:   The given expression is y2=36+xz.   The expression of the distance of a point from the...

Q: Use the graph of the function to find the domain and range of f.

A: The graph of f is as shown below :    

Q: Use a graphing utility with a viewing rectangle large enough to show end behavior to graph the polyn...

A: fx=-x4+8x3+4x2+2 Here, Degree of given equation is 4 (even) and leading coefficient is -1 (negative)...

Q: Confirming a graph The graph of ƒ(x) = sinh x is as shown . Use calculus to find the intervals on wh...

A: Clearly from the graph the following observations can be made from the curve. The slope of the sinhx...

Q: Write each number in decimal notation without the use of exponents. 6.8 x 10-1

A: Consider the scientific notation is of the form. a×10n The number in the scientific notation is writ...

Q: For some tasks, a sigmoid learning curve is used to model proficiency. Suppose the percent 100 profi...

A:

Q: dx Vi -x 0.

A: we have to integrate the definite integral  ∫01dx1-x2  

Q: 3. Find cos2020 r dr.

A: Given: I=∫02πcos2020x dx We have to find the given definite integral.

Q: I need help finding F'(x) and f''(x) when f(x)= 5x^3-2/x^2

A:

Q: 3. Copy the following equation to the right of where it appears on the page. -2(3x – 1) + x = 14 – x...

A: According to the question, we have to copy the given expression. As the above expression is algebrai...

Q: Sketch a rough graph of P'(x) for 0

A: The curve of the graph has a vertical tangent (slope is infinity) at x = 0. So, the graph of P'(x) i...

Q: Determine whether the below given  statement makes sense or does not make sense, and explain your re...

A: Given: 3x+15=14 To determine: "The given equation can be solved more easily by multiplying both side...

Q: Hi need help figuring out the answer please

A:

Q: Use the given graph of f(x) = x² to find a number 6 such that if Ix - 1| < 8 then |x2 – 1| <. (Round...

A: Given: fx=x2 and graph of function as To find: The number δ such that if x-1&lt;δ then x2-1&lt;12.

Q: Simplify 6(-4) - 5(-3) / (9 - 10).

A: According to the question, we have to simplify the expression 6-4-5-39-10. As the above expression i...

Q: Find the volumes of the solids generated by revolving the regionsbounded by the lines and curves abo...

A: The solid generated by revolving the region enclosed by the curve x=cosπy4 and the line x= 0  The re...

Q: 7-

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.