. The Minimum point of y = x3 3x+6

Q: Evaluate the integral: A B C D H|m 1 6 1 |ო 3 √ sin S 1 6 sin(3x)cos(3x) dx

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Q: 2 Let f(x)=√3x-2 on the interval axis about the y-axis and find the volume of the resulting solid.…

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Q: What is the differential equation corresponding to the general solution y² = Cx³. dy 2y = A dx 3x dy…

A: solution:-y2=Cx3where C is only one arbitrary constantdifferentiate both…

Q: How many antiderivatives does a function of the form f(x)=x" have when n*0= A) infinitely many (B)…

A: We have to choose option find antiderivative

Q: =√x, x=4 and the x-axis, the limits of integration are: If a horizontal element is used to find the…

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Q: (x+1)x (x+2)(x-1)² If f @ 1/1 1/1/0 93 B C D 9 . - 2 3 2 9 3 - 2/3 . 93 A B 421 + + x+2 C (5-131].…

A: Explained below

Q: If (x+1) dx (x+2)(x-1)² S -=S= A B + x + 2 + x-1 C (x-1)2 dx, the values of A & C respectively are:

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Q: Given A B 1 -dx, determine all value/values of P for which the improper integral converges? to…

A: Using p-test form infinite limit we know that:  For a>0: If p>1 then ∫a∞1xpdx converges. Here…

Q: √²/pdx. хр (1,00) B {0,1} C) (-∞0,00) D (-∞,1] Given (Α dx, determine all value/values of P for…

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Q: formula for the sum of the first n terms of a geometric sequence to find the sum of the first 11…

A: Given query is to the sum of the 11 terms

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1 (A) 1 unit² B -unit² 3 -…

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Q: Determine the 3rd derivative of the given function f(x) = (3x² - 5x + 6)4.

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Q: 1 √√√√x + x S Solve the integral: A m/1+x³²|+c C {/in/1+x²³ | +c B © 6in/5+x³³| +C Ⓒ √I/1 .…

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Q: Find the area bounded by : f (x)=e*, g(x)=e* and x=3. A (e²-1)² e2 sq. units B (e³+ 1)² e3 sq. units…

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Q: The general solution of (D³-5D²-6D)y=0 is Ay=c₁+c₂е¯x + c3e6x By=c₁ex+c₂e²x + c3e³x Ⓒy=c₁+c₂e²x +…

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Q: Given than f(x) dx = 4 and A None of the given choices ℗ 25 (2) dx = [1 (2) de B f(x) © f (x) dx =…

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Q: Determine the case of the following proper rational function after simplification: x + 2…

A: We have to find out simplification

Q: What kind of polar graph has the equation r = 3 ? * cardioid lemniscate circle rose petal

A: Solution: equation r=3

Q: Problem Solving: Prob. 1 A block of mass M = 10 kg is sitting on a surface inclined at angle 0 =…

A: Given that M= 10 kg and coefficient of static friction = 0.5 1. Minimum force necessary to prevent…

Q: In the indefinite Integral in(cosh x + e*)- integrand? A sinh x + ex B In(cosh x + e*) In(cosh x +…

A: What is the integrand

Q: Which of the following is NOT a method for finding volume of solids of revolution? (A) shell method…

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Q: 2x-1 a. √ (2x + 1) e ¹-¹ dx

A: The given integral is ∫2x+1e2x-1 dx We solve the integral using integral by parts formula. From…

Q: Practical Question: An object is moving horizontally with the speed of 50 m/s. When the object at…

A: Projectile motion is the motion of an object projected horizontally into the air and moving…

Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

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Q: Solve the integral: √√ 3√x dx x²

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming 1+z² Ⓒ √ 1 + 2/²/d= (A) -dz…

A: First of all, note that sec x=tan2x2+11-tan2x2⇒sec x+1=tan2x2+11-tan2x2+1⇒sec…

Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

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Q: (D5+ D4-7D³ - 11D²8D-12)y = 0

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Q: Using the method of variation of parameters, the form of a particular solution Yp of…

A: Here, the given DE is: (D2+25)y=4x2-3e5x

Q: etermine the area bounded by f(x)=x²-x and x-axis. 1 A unit² 2 B unit² 1 unit² 1 unit² D

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Q: y" - 3y' + 2y = 6

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: the line y=x-1and y=(x-1)3 intersect in the points (0,-1),(1,0) and (2,1) the line y=x-1 is below…

Q: The given function v = ln (xy) + ex+y Determine Ov/ox

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Q: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

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Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A: Given that , fx=x2+1 and gx=-x2+2x+5 find the volume of solid generated by revolving the region…

Q: 6. Find a²z дгу of z = In(xy)

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Q: Q/IF 3= sin(X) (²314) y = 3² sin(x) cos(x) Prove that

A: To find y':

Q: Question 10 Let f(x)=√3x-2 on the interval volume of the resulting solid. 43x 135 83m 125 83x 135…

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Q: 2) Find the standard deviation of the population sample. 2, 4, 7, 12, 15 3) Find the variance for…

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Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 (A) S= -dz 1+z² ® √ ²²+2…

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Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

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Q: O O O O It is reflected over the x-axis and shifted right three units. It is reflected over the…

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Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

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Q: What are the dimensions of the rectangular field of maximum area that can be fenced with exactly 500…

A: First make the equation of area in terms of breath or length then diffrenciate for maximum area .

Q: Given A B C D f(x) dx = 0 and 11 6 0 ¹² f(x) dx = 11 6 I 11 5 55 6 evaluate S²3f(x) dx - ₁2f(x)dx.…

A: we have to find the integral

Q: Determine the area bounded by f(x)=x²-x and x-axis. Ⓒ / unit² A ® B / unit² © unit² D -unit²

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Q: the indefinite Integral In(cosh x + ex)- A In(cosh x +ex) Sinh x + e* cosh x + ex (В sinh xtex sinh…

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Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: Given g is a differentiable function and range of g is on the interval I and  F is antiderivative of…