Let f(r) be the function defined by a r > 3 f(r) = 1 x < 3, 3' Find the value of a if lim f(x) = lim f(x) 23+

Q: ∫ 2y dx + 3x dy   where d is described by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A: Consider the given integral is, ∫2ydx+3xdy The above equation is of the form M=2y and N=3x. Then, by...

Q: You want to buy a $28,000 car. You can make a 10% down payment, and will finance the balance with a ...

A: Amount = 28000 Down payment = 2800 Financed amount = P = 28000-2800 = 25200 r = 0.04/12 = 0.0033 (co...

Q: Find a function of the form y A sin(kz) + C or y = A cos(kr) + C whose graph matches the function sh...

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Q: integrate (x^2)/sqrt(1-x^2)

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

Q: I'm not sure if this is correct.

A: Initially we will find the graph of the given function and it's inverse.  

Q: Write the complex number 0.6(cos 100° + i sin 100°)in rectangular form. If necessary, round to the n...

A: The given complex number is 0.6cos100°+isin100°.  

Q: 3. A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At...

A: Diagonal of Square = √2 * Side Perimeter of Square = 4* Side Area of Square = (Side)^ 2

Q: Evaluate the limit using L'Hôpital's Rule. In (3x) lim (Give an exact answer. Use symbolic notation ...

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Q: 18,19,20 step by step

A: fx=-2x+62+4 Compare the above function with fx=ax-h2+k. a=-2,h=-6 and k=4 from the above function it...

Q: Suppose a gift basket maker incurs costs for a basket according to C(x)=18x+220. If the baskets are ...

A: Given  C(x)=18x+220 The baskets are sold for $43 per basket.    

Q: 2. This exercise uses the population growth model. The count in a culture of bacteria was 400 after ...

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Q: Find the values of a and b that makes the following function differentiable. S(2) – {3e¬3 la(6 – 2)²...

A: Given fx=3ex-3      if x&lt;3a6-x2+b   if x≥3

Q: Find the constants a, b, c, andd so that D + D4 + aD3 + 5D2 + cD+ 4d y= 0 has a solution of the form...

A: Given differential equation is, D5+D4+aD3+b2D2+cD+4dy=0             ...(1)

Q: Find two solutions of the equations. Please give me the answers in degrees and in radians. a) cscθ =...

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Q: 2. a n=

A: The arithmetic sequence is -1, 1, 3,......  

Q: The weightlifter does more work in raising 300 kilograms above her head than Atlas, who is supportin...

A: Given information: The weightlifter does more work in raising 300 kilograms above her head than Atla...

Q: Find r for the infinite geometric sequence. Determine whether the sum will converge. -24, -12, -6, -...

A: -24 , -12 , -6 , -3 , .....

Q: If a ball is thrown with a velocity 48 ft/s, its height in feet t seconds later is given by y = 48t ...

A: Given that if a ball is thrown with a velocity 48ft/sec, its height in feet t seconds later is given...

Q: Find two functions f and g such that (fo g)(x) = h(x). 1 h(x) x + 5 (f(x), g(x)) = Need Help? Read I...

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Q: (a) Use differentiation to find a power series representation for 1 f(x) (6 + x)2 (-1)"+2(n+1)x" 6"+...

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Q: Find the sum of the first 12 terms for the follov a2=3, a4=7 The sum of the first 12 terms is

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Q: Find ag and a, for the arithmetic sequence. a,=x, a, = x+3

A: a1=x , a2=x+3 Formula an=a1+(n-1)dd is the common difference

Q: 2x9 21. Evaluate ſ dx 1+x10

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Q: 6. The pH reading of a glass of liquid is given. Find the hydrogen ion concentration of the liquid. ...

A: Given pH of of part a,b we need to find H+ ion concentration  by using formula.of pH

Q: Please state whether the following is true or false.

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Q: Suppose that demand for local cable TV service is given by p = 118 - 0.4x where p is the monthly pri...

A: As per bartleby guidelines only first three subparts are to be solved. Please upload other parts sep...

Q: Determine whether the Mean Value theorem can be applied to f on the closed interval

A: Given function, f(x)= 1-x , [-8, 1 ] Means value theorem states that,  Suppose f(x) is a function th...

Q: Assume that y is a function of x. Consider the curve defined by ln y=x^2+xe^y. Find the slope of the...

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Q: Graph and find the domain

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Q: integral calculus

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Q: Applications of Integral Calculus Find the total utility equation for a consumer if the marginal ut...

A: Given  marginal utility MU = 12 - 9Q To find total utility equation of a consumer

Q: Determine whether the series is convergent or divergen 3n+1 a. En=1 5n +4 5n b. En=1 00 en

A: Given: The series, a. ∑n=1∞3n+15n+4b. ∑n=1∞5nen    

Q: The goal of this problem is to evaluate the improper integral: (a) First, decide why the above integ...

A: Given, ∫-∞0x2exdx This is improper integral, So, We can write, ∫-∞0x2exdx=limt→-∞∫t0x2exdx limt→-∞∫t...

Q: Evaluate, do not round answers! Use substitution when appropriate. n/4 n/2 a) S sec 0 tan 0 de b) xV...

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Q: (a) Perform the division of polynomials P(x) D(x) R(x) Q(x) + D(x) with the degree of R(x) less than...

A: Solution :-  It is given that  p(x) = x4+81and D(x) =x2-3 now we have to divide the p(x) by D(x)   

Q: Ernd the area of the shaded rearon o the r= cos 2A 01011 4 1 0--1- 7ven ST 041 112 1世學1S 01ル 6. 10 |...

A: The equation of the curve is r=cos2θ.  

Q: 17 April shoots an arrow upward and into the air at a speed of 32 feet per second from a platform th...

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Q: A child learning to save money invested a capital of $ 250 at a nominal rate of 0.0825 with simple i...

A: Amount earned is 11.98 that is the interest earned WE use simple interest formula I=Pnr365where P is...

Q: Write an equation for the parabola with a vertex (-5,3) and directrix x= - 8. An equation for this p...

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Q: find the particular solution of y"+ 12y+36y=0 with y(0)=3 and y'(0)= -36. A y= 3(1+6x)e-6x y=3-1(9- ...

A: Given: y''+12y'+36y, with y0=3 and y'0=-36 To Find: Particular solution of the given differential eq...

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region a...

A: Given: y = 64-x2  To find: Volume of the solid formed by revolving the region about the x - axis.

Q: The voltage V​ (volts), current I​ (amperes), and resistance R​ (ohms) of an electric circuit like t...

A: It is given that   V is increasing at the rate of 5 volt/sec  I is decreasing at the rate of 1/4 ​am...

Q: Please state whether this is true or false.

A: Given, ∫abfxdx = area above x-axis - area under x-axis   We have to identify the truthfulness of the...

Q: Given the defined function f(x) 2x +8, x 3

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

Q: Differential Applications y = f (x) "KOPMA UNPAD" faces the demand function P = 100 - 4Q and the tot...

A: Given, Demand function p=100-4Q Total cost  C=50+20Q

Q: Differential calculus y=f(x)

A: Here we have to find the derivative of the given two functions.  In first function we use chain rule...

Q: improper integrals

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: