Find the derivative of: — 2 sin² (9x5). Hint: sin²(x) = [sin(x)]²...so use the chain rule (twice!).

Q: 10. Determine the convergence of the following series using the root test. If the root test is…

A: Given data:- The given equation, ∑n=1∞n+1n+2n

Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

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Q: Boyle’s Law says that the volume V of a gas atconstant temperature increases whenever the pressure P…

A: Given: Volume and Pressure are inversely proportional. P=14.7lb/in2when V=1000 in3 To find: V when…

Q: Write the function whose graph is the graph of y = x2 , but is shifted left four units and down 2…

A: The original function: y=x2 To write a function whose graph is the graph of original function but…

Q: Solve equation log5x+log(x-1) = 2 without using a calculator.

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Q: II. Give the indicated derivative 1) find the 27th derivative of cos x

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Q: Graphing a Linear FunctionGraph the linear function f1x2 = - 3x + 7. What are the domain and the…

A: Given, fx=-3x+7

Q: Graph the functions ƒ(x) = sqrt(x )and g(x) = sqrt(1 - x) together with their (a) sum, (b) product,…

A: Given data:- The given functions is, fx=xgx=1-x

Q: Consider the ellipsoid x² + y² + 3z² = 8. Find all the points where the tangent plane to this…

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Q: Use the disk method to find the volume of the solid obtained by rotating the region bounded by x = 1…

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Q: Consider the following limit statement: lim (9x-3) 15 x → 2 Find the corresponding value of 6 when &…

A: givenlimx→39x-3=15

Q: Find the directional derivative of f at the point P in the direction of a. P(4,0); f(x, y) = 4x³y³;…

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Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y - 2z subject…

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Q: Compute f' and find an equation of the tangent line to the graph at x = a. f(x) = 9x-³, a = 5. (Use…

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Q: Use the formula for nPr to evaluate the expression 8P0.

A: Given: The given expression is:  8P0 Formula Used: Prn = n!(n-r)!

Q: 2. y = -8 ln x 4. f(x) = ln(6x) 6. f(x) = ln |5x| 8. y = x¹ ln x In x 10. y 1) 2) +8 = In A - In B.

A: Solution

Q: You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart.

A: Given: Total number of cards = 52 Formula used: Probability = Number of favourableNumber of outcome

Q: Engineers must consider the breadths of male heads when designing helmets. The company researchers…

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Q: Find the slope of the line containing the points (3, - 2) and (1, 6).

A: Given data:- The given points of line is, 3, -2 and 1, 6

Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 13 tan (²); P(-14,14);…

A: The given function is fx,y=13tan-1yx. To find the directional derivative, find the gradient of f.…

Q: Find the particular solution of each of the following. (4+sine)y'=e*(6soc² e* - ycose); y(ln x) =…

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Q: Use the Fundamental Counting Principle to solve:An ice cream store sells two drinks sodas or milk…

A: Given data:- The given store gives two types of drinks Soda or milkshakes. There are given four…

Q: (a) J x² dx 3x + 2 x + 7 (b) 6) [ √2+1 da dx

A: Since multiple questions are asked, I am answering first question

Q: If you roll a 1-m-diameter wheel forward 30 cm over levelground, through what angle will the wheel…

A: Given data:- The given you roll a 1-m-diameter wheel forward 30 cm over level ground. Formula used,…

Q: Given the following functions: f(u)=u^5/2 and g(x)=x^6+1. Find f(g(x))= f′(u)= f′(g(x))= g′(x)=…

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Q: Sketch a graph of the function f(x) = 2 sin (7x) 2 - 2.

A: The function is given by fx = 2sinπ2x-2 To determine: The sketch of the graph of the function.

Q: Find the exact length of the curve. 1 y² = 16(x + 1)³, 0≤x≤ 3, y>0 109/109 (217 217 (21717 X

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Q: How many different four-letter passwords can be formed from the letters A, B, C, D, E, F, and G if…

A: The letters A, B, C, D, E, F, and G.

Q: Find the equation of the plane that passes through the point (2, 1, -3) and is tangent to the…

A: Given,             x2+4y3+3z2=35 ⇒x2+4y3+3z2-35=0

Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt

Q: Evaluate the expression.

A: Given: The given expression is: C15·C27C312 Formula Used: Crn = n!r!(n-r)!

Q: 2. Find the 2nd derivative of sin (x²-1) y *2cos(x^2-1) 4x^2 tan(x^2-1) 2cos(x^2-1) + 4x^2…

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A: Question: Please have a systematic way of solnerate solution of the first-order differential…

Q: If f (x) = x2 - 2x, find f (a + 1) and f (a + 2).

A: Given fucnction, fx=x2-2x

Q: If f(x, y, z) = 3xy + z² and u is the unit vector in the direction of (3, -3, -4), then the…

A: This question can be solved using the concept of derivatives and vector.

Q: Use the formula for nPr to solve:How many arrangements can be made using four of the letters of the…

A: Given: the given word is = COMBINE Total number of words n = 7 Number of used letters = 4 Formula…

Q: Question 2 Determine the values of a for which the following system of linear equations has no…

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Q: Use the Fundamental Counting Principle to solve:A restaurant offers the following lunch menu. Main…

A: Given data:- A restaurant offers the following lunch menu:- Main Course      Vegetables…

Q: Evaluate the limit 16x √x lim x 16 4 Number

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Q: Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the…

A: Concept used: Graphing A graph of a function is a line that represents the function on a coordinate…

Q: Find the area of the shaded region. f(x) = x² - 4x³ + 12x². g(x) = - 3x +90 The area is (Type an…

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Q: Find the parametric equations of the intersection of the planes x + (y − 9) + z = 0 and −x + (y + 9)…

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Q: find f + g, f - g, f # g, and fgfor each pair of functions. State the domain of each of these…

A: Given, fx=3x2+x+1gx=3x

Q: Rewrite the following expression in terms of exponentials and simplify the result. (cosh 3x - sinh…

A: We need to rewrite the given expression in terms of exponentials.

Q: Use the formula for nCr to evaluate the expression 7C7.

A: Given: The given expression: 7C7. Formula Used: Crn = n!r!(n-1)!

Q: compute the acute angle formed by the asymptotes of the hyperbola x^2-3y^2-8x=14

A: Explanation of the answer is as follows

Q: If you are dealt one card from a standard 52-card deck, find the probability of being dealt a king.

A: Given data, No. of cards drawn 1. n(A)=4 n(S)=52

Q: In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3,…

A: a) ∆x=b-an

Q: Use the geometrical series formula to evaluate the following: k=2 3 5k

A: Given :- ∑k=2∞35k

Q: 3. Determine whether the sequence an = n cos ní is bounded, bounded above. bounded belew, or none of…

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