r = 6 - 5cos0 O circle

Q: Suppose that it is given to you that f′(x)=(x+5)(10−x)(15−x) 1.The first inflection point (from…

A: Given that,     f'(x)=x+510-x15-x

Q: Evaluate the following limit: lim (7,y)→(0,0) 5æ6 + 6 sin°(y) 14x6 + y6 3 4 11 15 2 3 The limit does…

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Q: 2. g'-yso ylo)=2 gilo): -2 y'Co)= y'(0)= -2 : -2

A: Given: y''-y=0, y0=2, y'0=-2 So, we can also write as: D2-1y=0   The auxiliary equation is: m2-1=0

Q: Find the area bounded by the graphs of f(x)=x+2, g(x)=3x²+5 , x=-1 and x=1.

A: Explanation of the answer is as follows

Q: Find all the local maximum and minimum and saddle points, with their values, for the function f(x,…

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Q: t) A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A: solution

Q: f(-9) = 0 f(-1) = 0 f(2) = 2 f(4) = 4 f(6) = 3 lim f(x) =∞ lim f(x) =-∞ X--5+ lim f(x) = ∞ lim f(x)…

A: Concave up:(-∞, -5) : f''(x)>0function is decreasing in (-∞, -9)f'(-9)=0and function is…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of  PQ.…

A: Given problem:- Find the directional derivative of the function at P in the direction of PQ. f(x, y)…

Q: Find all the local maximum and minimum and saddle points, with their values, for the function f(x,…

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Q: Determine that area. 4. A solid is obtained by rotating about the x-axis. The curve is given to be…

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Q: The gcd of 687 and 24 is: 01 O 11 12 3

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Q: 50) If f(x) = r° cos(x³), then f() (0) is d) 5! а) 0 b) 1 с) 3! e) f(5) (0) does not exist. 51) If…

A: f(x)=x3cos(x3)f(x)=x3∑n=0∞(-1)n(x3)2n(2n)! f(x)=x31-x62! +x123!+...f(x)=x3-x92!…

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Q: Find the Laplace transform of f(t) = u(t – 4) · e' F(s) %3D 8-2

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Q: What is the solution of the differential equation y' + 6y + 25y = 64e-3 ? %3D

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Q: 4. A ladder 25 feet long is leaning against a vertical wall. The base of the ladder slides away from…

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: x³3-* dx -x³3-*In (3) + 3x² 3¬× ln²(3) – 6x 3¬×ln³ (3) + 6 3¬× In*(3) + C A B -x³3¯* ln(3) + 3x² 3¯*…

A: Let's find.

Q: 8n-4 Determine if the sequence An converges or diverges. If the sequence 67 –4 converges, to what…

A: Given : an=8n-46n-4   To check : an converges or diverges

Q: Г(x3 + 2х — 1) cos 4x dx A .3 13 x (3x² 13 sin 4x + 4 |cos 4x + C + - 4 32 16 128 B (x³ (3x² 13 |cos…

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Q: Find the solution set of the inequality 5x2 – 2x + 12 < 6x² – 3x – 18. - Select one: а. [—5, 6] b.…

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Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: Use the Ratio Test to determine the radius of convergence of Eo . x" (Use symbolic notation and…

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Q: a) Approximate the area under graph (a) of f(x) = 3/x over the interval [2,10] by computing the area…

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Q: a51 - Find ax2@y3 if f(x,y)-x.e z

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Q: Which of the following is the inverse of the functionf : [0, ∞) → [3, 0), f(x) = 2.x² + 3? Select…

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Q: d y Find dx? |(-1,2) if x² + y' = 9

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Q: For the series k! k2 compute the partial sums: S1 = S2 S3 = S4 = You will have to compute these as a…

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Q: )Let f(x) be function. What will be the asymptote, if lim f(x) = ±o? %3D O Vertical line O…

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Q: Find the relative maximam/minimum values of the fuction f(x)=X-2 State where the function is…

A: Given,            fx=x-2x+2To find : Find the relative maximum/ minimum values of the function.…

Q: (5x) сos (Зa')dx COS

A: LetI=∫cos5xcos3xdxI=12∫2cos5xcos3xdxWe know…

Q: The series > cos" (2) is divergent. n=1 This statement is true by the test for divergence. This…

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Q: 8. A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: topic - application of derivatives

Q: The graph of f(x,y)=++13xy has X y -13ху O One local maximum point only. O One local maximum point…

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Q: 38) Assume that f(x) is a solution to the differential equation y' = 2x + y with f(0) = –1. Then…

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Q: Find the derivative. y = e2= . 8x3 24x?e2 + 16x4e2« – 1 O 2e2a . 24x? 24x e2 + 16x³e2* O 2xe2a…

A: We will find the derivative using Chain rule.

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: I am attaching image so that you understand each and every step.

Q: sin(x) dx Jo

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Q: Solve the differential equation with appropriate method. Finalize answer equated to ky^n. dy/dx + y…

A: Using bernoulli's differential equations, solve this differential equations.

Q: Omar is flying two kites. He has 95 feet of string out to one kite and 114 feet out to the other…

A: The objective is to find the distance between the kites.

Q: 4. Find the total differential of z = In(x + y), x= w, y = w². By how much will z change if w…

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Q: tan3 -dx sec x

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive.…

A: We will create a Lagrange's function to solve the problem.

Q: Consider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

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Q: Write the general formula for following alternating series in the form > an. n=1 5 5 - ... 8 10 11…

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Q: For the function g(x) =x - 9x° solve the following. 3 g(x) <0 .... Select the correct choice below…

A: The given function is: gx=x5-9x3 Solve  gx&lt;0

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: Which of the following gives the formula for the inverse of the function x + 3 f : R \ {-7/2} → R \…

A: I am attaching image so that you understand each and every step.

Q: Problem Problem LISI Nexi Plobem nt) Let I be the length of a diagonal of a rectangle whose sides…

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Q: 3+ dx

A: