Convert this identity to one using sine term(s) only. 1 - 2 cos2r = 2sin²r - 1 -1 - sin²r 1 - 2sin²r

Q: Given h(x, y, z) = 4Vx+ ln (y² + z²+1). (a) Find the directional derivative of h at the point (1,0, ...

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Q: Vx + 9 dx dy The answer should be in the form ' S S(x, y) dy dx, where a < x < band 81(x) < y < 82(x...

A: We will evaluate the double integral. 

Q: dx sin (7x)[7-cot2(7x)]

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of th...

A: The circle formed has the area  A=πr2...(1) Differentiating it with respect to t: dAdt=π2rdrdt...(2)

Q: Determine whether the alternating series converges. 2(- 1)*+1 k+ 1 2k + 1 k=1 O The series diverges....

A: Alternating series test: Suppose that we have a series ∑ an and either  an=(-1)nbn  or an=(-1)n+1bn ...

Q: Suppose that {a,} is a monotone sequence such that an 14 or increases - in this case we can't say w...

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Q: (x-1) y ' = y +2(x-1)3

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Q: Question (see above) EXAMPLE ONLY: 3. x? + 5x – 5 on [-6, 2] Proving that the function f(x) = x? + 5...

A: Solution is given below:

Q: Find the slope of the tangent line to the graph of the given function at the given value of x. Find ...

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Q: Below is the graph of y=3^x Translate it to become the graph of y=3^x+4-2 provide the points and h...

A: Given: -  Below is the graph of y=3x Translate it to become the graph of y=3x+4-2 To translate: - P...

Q: Find the derivative using the formula f'(x)= g'h + gh' 1. cos x cot x Let g= cos x, and h= tan x. ...

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Q: Show that each function is continuous at the point indicated. 1. f(x) = 3x? – 4x + 2 at x = 2 2. f(x...

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Q: 3. Find the derivative of the following functions using the increment method. (10 pts each) 6- 3x 1 ...

A: a f(x) = 1/2-x now using increment method f'(x) = limh→0 [f(x+h) - f(x)]/h f'(x) =limh→0 [1/ 2-(x+h)...

Q: Evaluate the slope of the function: (Please solve using limits) a. f(x) =x^2 + x - 2 ...

A: a)   f(x)=x2+x-2                       at       x=-1.5Here f(x)=x2+x-2Thenf(x+h)=(x+h)2+(x+h)-2We kn...

Q: dy = 6x– 2x + 1 cos y + eY %D dx

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Q: If s(t) = 2t-3t2- 12t +5, represent the position of a particle traveling along a horizontal line. De...

A: Let's find. 

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. ^2 cy? yz dx dz dy DNE -90 J-60

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Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A:  Given: x=13yy-3

Q: Please Find an equation of the line tangent to the curve defined by x^4+2xy+y^3=4 at the point (1,1)...

A: The given problem is solved below in detail.

Q: For items 1 to 4, identify which type of infinite series the given series belongs to. Then, use it d...

A: p -series ∑n=1∞1np and it is convergent if p&gt;1

Q: Calculating pressure-volume work A mixture of nitrogen and neon gas is expanded from a volume of 90....

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Q: The position of the particle at time t is given by s(t) – t- 16t + 63. The particle is moving from r...

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Q: %24 %23 - and r = 0. =D0. Find the area of the region enclosed by y = 5e*, y = 6e¯² and x = 0. 5- 4....

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Q: Find the derivative of the following functions using the increment method. *b. f(x) = 6- Зх 1 *а. f(...

A: Topic:- derivatives

Q: b) Evaluate the intergral. Show (with your work) that it is Cunvergent and give its Value or that it...

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Q: Set up the definite integral required to find the area of the region between the graph of y = 12 – x...

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Q: Calculate the integral approximations Ts and Ms for L'(In x)-2 dx. Your answers must be accurate to ...

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Q: et dx Ve²x+49

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Q: The position of the particle at time t is given by s(t) = t – 12t + 35. The particle is moving from ...

A: The position of the particle at time t is given by s(t)

Q: Express the repeating decimalas a fraction. 0.517838383838.. 0.517838383838... =

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Q: Evaluate the integral. /| x In(y) dA, R = [0, 11] × [1, e] (Use symbolic notation and fractions wher...

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Q: etermine the equation of the circle graphed below. 10 8. 6. 4 -10 -8 -6 -4 -2 4 6. 10 -2 -4 -6 -8 -1...

A: We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is...

Q: PROBLEM 2. Solve for the general solution term by term of the ordinary differential equation given b...

A: Topic - differential equation 

Q: 4. S (sint + cost t ) dt A - cos t + sin t + C C - cos t- sin t + C B cos t+ sin t + C D cos t- sin ...

A: 4. In this question, we need to find the integral.

Q: Suppose that a population of bacteria triples every hour and starts with 200 bacteria. Find an expre...

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Q: 2. Find the area of the region enclosed by y = 3.5x and z 9-y. %3D 2- 1- 1234 5 6 7 8 9 -1 of Use ho...

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

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Q: Suppose that the revenue from selling x radios is R(x) = 75x - dollars. Use the 10 function R' (x) t...

A: Here, the given revenue function is: R(x)=75x-x210⇒R'(x)=75(1)-2x10=75-x5

Q: Solve for the general solution of the equation: y'=xy

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Q: Find lim f(z) if 4x 1 472 < f(x) < + 3x for all z 5. T100

A: Apply sandwich theorem

Q: 1 1 V13+x 3 h. lim X→0 X + 4

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Q: 3 x³ – 64x e. lim 5 .2 е. X + 2x

A: Topic:- limits

Q: A function f has a removable discontinuity at x = c if limf(x) exists by f is not continuous at x = ...

A: Here, the given function is: f(x)=x-2|x|-2 So, function is not defined at x=2,-2

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A: Given

Q: 2x5y ' = y(3x4+y2)

A: For the solution follow the next step.

Q: A boat is being pulled toward a dock as shown in the figure to the right. If the rope is being pulle...

A: topic - application of derivatives

Q: A company's demand function of a product is given by : 10) p- 150 - 0.002 x ,where p is the price pe...

A: The revenue function, R(x) = x P(x), where P(x) is the demand function. R'(x)  is the rate of change...

Q: Watch the completing the square review videoe before answering the following question. When you comp...

A: The given expression is: x2-3x+1   As we know from the algebra; a+b2=a2+2ab+b2a-b2=a2-2ab+b2

Q: 6. Compute 1,= de for p= 0,1 10

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