2 is a critical number of the function f(x) = /2x – x². Select one: OTrue O False

Q: The partial derivative of a function of two variables are represented by f,(x,y) which is the…

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Q: inal the @ e w and cone an ave cof the Cuarve?

A: here i am providing my hand written solution

Q: Find the volume of the solid in R' bounded by y = x2, x = y?, z = x + y + 27, and z = 0.

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Q: How many ways are there to distribute r+s identical balls among five different children such that…

A: We need to find ways to distribute balls as asked.

Q: (r -4 ifx2 6. f) = 4

A: Given query is to find function is continuous or not.

Q: Find critical points of the function e(2 -3x) O x = 0, x = 1 O x = 1, x = 3 O x = 0, x = 2 O this…

A: Topic = Derivative

Q: Find the solution of the following Differential Equations 7) y+4y =0, y(0) = 2.8

A: Topic:- application of integration

Q: 3) What is the square root of -5?

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Q: Evaluate the integrals in the following questions using integration by parts for SincE In (x + x²)…

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Q: 16. (ho f)(x) (A) VAr – 1 (C) 4r² +1– 1 (B) 2r – 1 (D) 0 17. (fo h)(1) (A) VAr – 1 (C) 4r2 – 1 (В)…

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Q: 3. If water bottles are geometrically similar, how much more water will a bottle that is 50 cm tall…

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Q: Determine whether the function is continuous or discontinuous 5. f(x) =

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Q: Solve the following indefinite integral. Show complete solutions. 1. S (9z² + 14z – 2) dz -

A: ∫(9z2+14z-2)dz

Q: y" + 25 y = 10(cos(5t) – 2 sin(5t)), y(0) =1, y'(0) = 2. %3D %3D

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Q: csc? 20 cot 20 de

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Q: Calculate the surface area of the portion of the cylinder X+y 9 that lies betweenz=3 and z=6. O A.…

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Q: Consider the following differential equation. y" + 2y - 24y = x Proceed as in this example to find a…

A: We need to solve D.E.

Q: 1. Obtain the general solution unless otherwise instructed · (D5 + Dª – 7D³ – 11D² – 8D – 12)y = 0 -…

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Q: Sece. tano do seco Jsec'o -1 Seco . tanodo feco· Jtario feco. tono do Seco . tomo

A: we have to solve integration.

Q: -3 0 5] 1-3 0 5 18) 00 0 1 1 00 0 0 0 A) 5 B) 4 C) 3 D) 2

A: Consider the matrix

Q: Evaluate the integrals in the following questions using integration by parts for In (x + x²) dx

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Q: A car move with an initial velocity 60 km/h, then accelerate at 7000 km/h2 along a straight road.…

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Q: Problem #7: A rectangular garden is fenced on three sides, and the house forms the fourth side of…

A: Given problem:- A rectangular garden is fenced on three sides, and the house forms the fourth side…

Q: dy 2. When does the differential equation Cekt represent exponential growth? exponential dt decay?

A: We need to explain growth and decay.

Q: Find * L(e2t t2)

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Q: Find the volume of the solid above the region D={(x,y) : 0s Xs V27, 0s ys 27-x2) and between the…

A: Let's find.

Q: Using L'Hopital's rule, calculate the following limit: T-sin r lim, 0 O 1/6 O 1 O does not exist

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Q: "he following series is convergent: (8")(10") (7")(9") + 1 n=1 elect one: OTrue OFalse

A: Topic:- sequence and series

Q: -olve for two cases csc² 20 cot 20 de irst case Using u = cot 20

A: Topic:-  integration

Q: 161 n + e 20 n 2n + tan (103 n). CO The sequence is n=1 O divergent as its limit is o 161 O…

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Q: Q28- The value of e-(In+1 )n is a) (-1)" e--1 b) (-1)"e" c) (-1)" e-+1 d) (-1)" e-"

A: We have to find value of  e-(in+1)π

Q: Find the general form of f if f'(x) = - 5f(x). f(x) =

A: Given that,      f'x=-5fx

Q: [cos 3x cos 4x dx

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Q: A 5-meter-long ladder is leaning against a wall. If the bottom of the ladder is being pushed towards…

A: This is a problem related to derivative of the function and Pythagoras theorem. Based on the general…

Q: You make $8.45 an h before taxes? a) $278.85 b) $295.75 c) $302.07 d) $338.00

A: Topic:- algebra

Q: Vr2 – 2x – 3x (x² 4. lim 4x + 5 (72 25) ten2(r1 2)

A: first we will take x common from numerator and denominator, then take limit.

Q: Use either integration by substitution or integration by parts as needed to evaluate x²+1 B A x3+…

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Q: 1) A box containing a group of balls (blue and red) totaling 25 balls. If nother Five blue balls are…

A: Topic:- probability

Q: I. Evaluate the following. You are NOT allowed to use L’Hopital's rule. Vx² – 2x – 3x 3 - V11+ 4x 2x…

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Q: Evaluate: L-1 [2s-9) ls²+2)

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Q: |cos 3x cos 4x dx :

A: We have to find the given integral.

Q: Find all solutions to the equation. 2 sinx- cosx=1 Write your answer in radians in terms of t, and…

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Q: (y In a In y) dr + dy = 0 O In In y| + x Inx +x = C O In y = Ce" r* O y = eCe*z* O y = eCe*z ts)

A:

Q: Use the Alternatng feries Test to determne whether the alternating senes converges or diverges…

A: Explanation of the answer is as follows

Q: What is the absolute maximum value of the function f(x) = x' - 3x? on the interval [-2, 3] ? а. ) O…

A: We have to find the maximum value of the function

Q: 3. 4x 3 + dx

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Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: log, (cot-x) 3. lim 1- cosh(2") X -00

A: limit.

Q: What is the critical point?

A: The objective of the question is defination of critical point.

Q: Given f(x) =x²- 1, find the value f(x+h) - f(x). 2x + h - 2 2х + h

A: