Simplify the expression to a single trigonometric function. cot (t) csc(t)

Q: (a) If y=f(x) = 7e²+3x² - 20x-5, find the derivative f '(x).

A: given that,   y=f(x)=7ex+3x4-20x-5,   find the derivative of f(x)? formula:   ddx(xn)=nxn-1

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Q: fies a(t) = −9.8 + mv(t)², where v(t) is velocity, negative since the object is falling, and k is a…

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Q: Three hundred books sell for $40 each, resulting in a revenue of(300)($40) = $12,000. For each $5…

A: Given: Price per book = $40 Resulting revenue was (300)($40)=$12,000 For each $5 increase in price,…

Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy dx…

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Q: Find parametric equations representing the line segment joining P(-3, 2) to Q(2, -1) as (x(t),…

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Q: True or False: The following function is continuous on R. True O False f(x) = if x sin x 44

A: Given function:- fx=sinxif x<π4cosxif x≥π4

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: The limit lim h→0 f(x) a = = In(e +h)-1 h represents f'(a) for some function f and some number a.…

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Q: Example 4 (Calculator Active): For 0 ≤s ≤ 5000, the total amount a local college spends on printing…

A: NOTE: Refresh your page if you can't see any equations. . the given cost function is  where…

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

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Q: 8. Use the limit comparison test to determine the convergence of the following series; state what…

A: See this solution in below.

Q: 9x²9x + 54 x³ + 3x 1² dx

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Q: Evaluate the following limit: lim O O O 6x²+17x-3 lim x→∞ 5x²+14x-3 6x²+17x-3 lim x→∞ 5x²+14x-3…

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Q: Evaluate the following integral, showing all calculus and algebra work. 2x² √2x²+x=1d + x - 1 -dx

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Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

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Q: 1. y peax cosbx + peax sin bx ; a and b are parameters

A: According to given ,1st is solved.y=ϕeaxcosbx+ψeaxsinbxhere 2 constant then 2 times derivative

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A: Solution: Given an input-output matrix  The production matrix is X and Demand matrix is D

Q: Find an equation of the line containing the points 11, 42and 13, 82.

A: Given data:- The given points, 11, 42 and 13, 82

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

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Q: fxe* dx.

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Q: find the average rate of change from 2 to 3 for each function f. Be sure to simplify.   f1x2 = 3x -…

A: The average rate of change of function denotes how much the function changed per unit over the given…

Q: The variable interest rate on a student loan changes eachJuly 1 based on the bank prime loan rate.…

A: Given for the years 1992–2007, The rate can be approximated by the model r(x)=−0.115x2+1.183x+5.623…

Q: In 2004, an art collector paid $172,536,000 for a particular painting. The same painting sold for…

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Q: Graphing the Cube Root Function(a) Determine whether f1x2 = 23 x is even, odd, or neither. State…

A: Given function is cube root function i.e., f(x)=x3

Q: graph each function.f1x2 = 1 x

A: Given, fx=1x

Q: Determine fx and fy (A) f(x,y)=(sin(sqrtx))ln(y^2)   fx=__________________…

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Q: 11 Find the derivative of f(x) = -15sinx + +3√√x-5. X

A: Given function:- fx=-15sinx+11x4+3x7-5

Q: A chemical substance has a decay rate of 6.5% per day. The rate of change of an amount N of the…

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Q: Constructing an Open Box An open box with a square baseis required to have a volume of 10 cubic…

A: Note:- Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: (5) Find the center of mass of the region bounded by y = sin x between x = 0 and x = 7 above the…

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Q: the cable of a suspension bridge hangs in the form of a parabola. the distance between two towers is…

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Q: FIND F'(x) F(x) = 2 tanx 1+cosx

A: To differentiate the given function.

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 O A 4 OB.…

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Q: (a) Find the distance from P1 = 1 - 2, - 32 to P2 = 13, - 52.(b) What is the midpoint of the line…

A: Given, P1=-2, -3 and P2=3, -5

Q: 2 5. Sketch the region bounded by the curve x 2 = y and the line x = y + 2 and find the volume of…

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Q: lim 0-0 cos 0 - 1 20²

A: SOLUTION-

Q: 9. For what value of a is the following function continuous at every x? a x+6a, x22 8, x<2 Select…

A: Given query is to find the value of "a" that makes function continuous everywhere.

Q: (c) Let y = (In x)2. Compute y' by using logarithmic differentiation.

A: The given function y=ln x2x We have to find the derivative of y using logarithm differentiation.

Q: Find the interval of convergence of the following series Σ(-1)₂(x - 2)n n5n n=1

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Q: Which of the following equations can be made into a linear diff O A. (x² + xy)dy - (lnx - Iny)dx = 0…

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Q: 23. The accompanying figure shows the graph of y = -x² shifted to two new positions. Write equations…

A: Given: The figure shows the graph of y=-x2 shifted to two new positions. To write the equations of…

Q: Evaluate the sum 50 Σ(2 · k + 5) = k=1 50 Σ5₁(2. k+5). k=1

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Q: The equation y = 1x - c2 2 defines a family of parabolas,one parabola for each value of c. On one…

A: Given, y=x-c2                     ... 1

Q: (7) sin √x dx. (First substitution, then by parts)

A: The solution for the given integral is as follow.

Q: (b) Let y = (2x + 1) cos. Compute by using logarithmi dy dx

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Q: Find the directional derivative off at P in the direction of a. ƒ(x, y) = 5x²y³; P(2, 2); a = 3 i −…

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

Q: 11. Define what it means to say that lim g(x) = k. the motion y X-0 Choose the true statement below.…

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Q: -6 (-3,1) -5 86°F Sunny I 1 -4/ -3 -2 1 / -1 4 3 2 - 0 -1 -2 -3 -4 -5 -6 2 W Use the graph to…

A: Given query is to find the slope of the tangent line.

Q: Explain how the domain of g1x2 = 2x compares to thedomain of g1x - k2, where k Ú 0.

A: Given, gx=2x