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

Q: iven ·S. A (-∞0,00) B) {0,1} Ⓒ(1,00) D) (-∞,1] dx, determine all value/values of P for which the…

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Q: Find the volume of the solid of revolution generated when the area described is rotated about the…

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Q: The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The…

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Q: dx Evaluate: √(x+1) log(x+1) A In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C C In[log(x+1)] + C In 10…

A: Evaluate ∫dxx+1logx+1

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

A: Here we have to find the integral for finding the volume.

Q: If (A) (В (D (x + 1) dx (x+2)(x-1)² -ja دا | در 93 1 —— 9 9 . 3 2 3 x + 2 ++ x-1 (x-1)2 dx, the…

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

A: The functions are f(x)=x2+1 and g(x)=-x2+2x+5

Q: Question 12 We can apply General Power Formula of Integration on which of the following integrals? A…

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

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Q: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

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Q: S Given 1 хр for which the improper integral converges? A {0,1} (B (1,00) C (-∞0,00) D (-∞,1] dx,…

A: The given improper integral is: ∫1∞1xpdx Suppose p=1 then: ∫1∞1xdx=ln x1∞=∞ So, diverges.

Q: Determine the area bounded by the functions f(x) = (x+1)³ and g(x)=x+1. 1 A unit² ® 2-unit² B 1…

A: Please see the below picture for detailed solution.

Q: Determine the integral: [x²cosxdx

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

A: To find the volume of the solid.

Q: Given S dx, determine all value/values of for which the improper integral XP converges? (A) {0,1} B…

A: Please follow the next step.

Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+cosh2x A +C 2 + 2ln3 (3e)3+cosh2x 2ln3…

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Q: dy Classify the DE: xdx +xy= A) Separable and Linear (B) Separable but not Linear Linear but not…

A: Given differential equation is

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

A: The integration are

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

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Q: Solve the integral: Seln(2x² + 3x−4)³ (4x + 3)dx

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Q: y = x ¹ Arctan 4(x4)

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Q: a + bx² 3ax + bx³ dx

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Q: solve the following differential eqaution : (2x+y)dx-(4x+2y-1)dy=0

A: Solved below.

Q: Transforming Ⓒ A S B Ⓒ S dz ⒸS²+ de D dz 1+2² dx dz 2-222 dz using miscellaneous substitution will…

A: We need to choose correct option. As per Bartleby's Guidelines we can solve one question from…

Q: π Evaluate the integral: sin(3x)cos(3x)dx 11/13 B (c) D 1/1/00 H|m

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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: Evaluate: A B С) D (x+1) log(x+1) 1 -In[log(x+1)] + C In 10 1 -In 10 log² (x + 1) + C 2 In 10…

A: Given problem:-

Q: Let the integral be solvable' using trigonometric substitution. What is the correct choice of u…

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Q: Determine the general parametric solution of the following unsolved differential equations for the…

A: See the details solution in below

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: e integral: J √√√x+x F1+x X + C 1 x C 5 + C 6in|5+ x² +C 6

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Q: wen 1₁² / 0x хо A) (-∞0,00) B (1,00) C{0,1} D) (-∞,1] -dx, determine all value/values of P for which…

A: Here  , we have two cases when p=1 and when p not equal to 1.

Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

Q: y = 2 sin 3x 1+3cos2x

A: We are given  y= 2sin3x/(1+3cos2x)  We have to compute y'.    Before computing y', let us first see…

Q: cylinder cone pyramid if this triangle is rotated about the x axis, what figure is formed?

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Q: q13

A: We have to calculate the given indefinite integral

Q: x+2 Determine the case of the following proper rational function after simplification: (x2 -…

A: Here, the rational function is: x+2(x2-4)(x3-8)=x+2(x2-22)(x3-23)=x+2(x-2)(x+2)(x-2)(x2+2x+4)

Q: Which of the following can be determined given (A) L²³ F(x (f(x) + g(x) +h(x))dx g(x) dx © L² F…

A: We can solve this as follows:

Q: The improper integral A e B C) O D 1 if the 0 ∞ ex dx is

A: Solve the integration  From 0 to ♾️ for the integrand e-x.

Q: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

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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: Question 33 If g(x)=- A) B D d = 2√²-1 (2 ·S^*^[e'-In(21+1)]dt, find g''(x) - 4 (2x+ (2x + 1)² e*…

A: Solved below.

Q: We can apply General Power Formula of Integration on which of the following integrals? A / fes…

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Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: consider9x2+6x-7=9x2+6x+9-16=9(x+3)2-16 let u=x+3⇒du=dxThen9(x+3)2-16=9u2-16

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

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Q: Let f(x)=√√√3x-2 on the interval √[²/3, ¹1] y=1 and y-axis about the y-axis and find the volume of…

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Q: Find the area bounded by : f(x)=e*, g(x)=e* and x=3.

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Q: Determine the area bounded by f(x) = x² — X and x-axis. 1 A -unit² B -unit² Ⓒunit² 2 Ⓒ -unit² 1

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Q: Find the volume of solid generated by revolving the region bounded by g(x)=x²+2x+ 5about the x-axis.…

A: Given:      fx=x2+1      gx=-x2+2x+5  Volume of solid revolving around the region is…

Q: That statement "We can use the General Power Formula of Integration for indefinite integrals…

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