4. y = x²(cos(lnx) — sin(lnx))

Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

A: We have to find part 1,2 and 3.

Q: Determine how much time is requiredfor an investment to double in value if interest is earned at the…

A: Note:- FV = PV 1+Rnnt Here, FV denotes Future value, PV denotes present value, R denotes rate and t…

Q: C) Evaluate m√m - 1 dm D) Evaluate 32 dy

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Find an equation of the tangent line to the curve y=4x at the point (1,4)  Tangent line: y=

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

Q: Let F(x) = f(x7) and G(x) = (ƒ(x))¹ . You also know that a = 7, ƒ(a) = 2, ƒ'(a) = 15, ƒ'(a¹) Then…

A:

Q: Explain how to find a particular term in a binomial expansion without having to write out the entire…

A: Binomial expansion is to expand and write the terms which are equal to the natural number exponent…

Q: Consider the ellipsoid x² + y² + 4z² = 41. The implicit form of the tangent plane to this ellipsoid…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with…

Q: Find the derivative of the function. f(x) = arcsin (et) f'(x) = Find the domains of the function and…

A: To find out the derivative of the function.

Q: (1 + 1) ds + 2s = 3(1 + 1) + 12. (t 1 (t + 1)²¹ t> -1

A:

Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Find the dimensions of the region which enclose the maximum area

Q: 9x²9x + 54 x³ + 3x 1² dx

A:

Q: Find the x-intercept(s) of the following function. f(x)=x² - 4x +3 Give your answer as ordered pairs…

A:

Q: ✩ lim √25x² +279x+690 15x² +976 соех 1 2 O

A:

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

A:

Q: Use the formula for nCr to evaluate the expression 11C4.

A: Given data:- Here, n=11, r=4 Use formula:- Crn=n!r!(n-r)!

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: Use synthetic division to find the quotient and the remainder when the first polynomial is divided…

A: See the details solution in below

Q: Sorry forgot to specify, find the zeros

A:

Q: Find the equation of each hyperbola whose center is at the origin. Find the equation of the…

A:

Q: Figure shows a U.S. roulette wheel that has 38 numbered slots 1 through 36, 0, and 00. Of the 38…

A: Given data, No. of cards drawn 1. First spin ......Probability of occurring red n(A)=18 Second…

Q: 64. Consider the length h of the perpendicular from point B to side b in the given triangle. Show…

A: Given data:-

Q: Set f(x) Question 1 Solve the equation f'(x) = = 0. If there are more than one solution, separate…

A: Explanation of the answer is as follows

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

A: The given differential equation is x-ytan-1yxdx+xtan-1yxdy=0

Q: Rewrite the following quadratic function in vertex form f(x) = a(x − h)² + k. f(x) = 6x² - 6x +1…

A: Given query is to find the quadratic form of the function n

Q: f sect x tan²x dx

A: Given, ∫sec4xtan2xdx

Q: Find the directional derivative of f(x, y, z) = yz + x¹, at (3, 2, 1) in the direction of = + + k 7…

A: Given Find gradient

Q: A national census bureau predicts that a certain population will increase from 31.7 million in 2000…

A:

Q: Use the formula for nPr to solve:A corporation has ten members on its board of directors.In how many…

A: Given: n = 10 r = 4 Formula Used: Prn = n!(n-r)!

Q: Does the parabola y=2x^2 -13x + 8 have a tangent whose slope is -1? If so, find an equation for the…

A: Topic- Slope of tangent and equation of a line We are given an equation of the parabola y=2x2-13x+8…

Q: 9. Determine the convergence of the following series using the ratio test. If the ration test is…

A: Ratio Test

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A: Given lines are L1: x=2-t ,  y=3+5t, z=4+3tL2: x=4t, y=1-20t, z=4-12t

Q: Find an equation of the tangent line to the graph of the function f defined by the following…

A:

Q: On a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m³, length 88.6…

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Q: f(x)= 9x x2+8x + 15 Vertical asymptotes: x= -3, x=-5; Horizontal asymptote: y = Vertical asymptotes:…

A: Topic:- application of derivatives and calculus

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

A: Given, fx=-3x+7

Q: f(x) = b сos(x) - 2 3x² - ax + b 2x - 4a { x ≤ 1 ax+b 1 2

A:

Q: Assume that ƒ(x) is everywhere continuous and it is given to you that ƒ(2) = −7 and f(x)+7 lim x→2…

A: Given query is to find the equation of the tangent

Q: {²22-1 xx² if x ≤ 3 if x > 3 Calculate the following limits. Enter "DNE" if the limit does not…

A: Given query is to find indicated limits.

Q: Use the formula for nCr to evaluate the expression 4C4.

A: Given: The given expression is:  4C4. n = 4 r = 4 Formula Used: Crn = n!r!(n-r)!

Q: Consider the integral given by Using the following definition of the integral Ax n 4 [ (x² + 2x - 5)…

A: Solution

Q: A right triangle has base a meters and height h meters, where h is constant and a changes with…

A: Given query is to find the relationship between rate of change of angle and  rate of change of base…

Q: Find a parametrization of the parabola x = y². Don't forget an interval for the parameter. (Hint:…

A: Please see the below picture for detailed solution.

Q: 2. y=x+c₁e* + C₂е¯x

A: Given :y=x+c1ex+c2e-x

Q: Enter your answer as an ordered pair. Provide your answer below: f(x) = 7x² - 12x - 8

A: The given function is  f(x)=x2-12x-8

Q: Find the relative extrema of f(x)=32x² - 4x². Find the absolute maximum and absolute minimum of the…

A: solution is given below..

Q: In this exercise you will conclude that a limit does not exist by computing the limiting using two…

A:

Q: Use implicit differentiation to find дz дх дz ду = = дz дх and дz ду ln(xy + yz + xz) = 5, (x > 0, y…

A: see below the answer and calculation

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: a. b. C. S e. sin ²0 S de cos²0 S dx x(x²+1) d. 0 cos(20 + 1 S 9dv 81-v4 x3 x2–2x+1

A: