Show if the following limits produce an indeterminate form. Then, evaluate the following limits. lim (3²-2x+1) where a and b are nonzero constants x-1

Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

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Q: Transforming S Ⓒ √ 2²-22²2 =2 A -dz 1+z² z²+z B -dz 1- © S с © S D N dx using miscellaneous…

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Q: = 4 R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

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

A: Let's find volume of solid when curve rotated about x axis.

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

A: Volume

Q: Transforming S dx secx + 1 using miscellaneous substitution

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Q: Evaluate: L{cos(3+2t)} s cos32sin3 A s²+4

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Q: Which of the following can be determined given Ⓒ [² (4f(x) + 9h(x)) dx 3 ® √²³((x) + B © ²(f(x) -…

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A unit² ℗ 1/2 B D unit²…

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

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

A: Using the Leibnitz rule:

Q: Evaluate the given definite integral [ 2x³ – 6x² dx, from x = 1 to x = 2 X²

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Q: dx Transforming S using miscellaneous substitu secx + 1 A S²= 2-2z² -dz 1+z² 1+z² B 1-z² 1-z² © √ 1…

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Q: Compute the Fourier sine series for the given function f. a) f(x) = x², 0<x< π

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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: Find the average value of the function f(x, y) = xy over the triangle with vertices (0, 0), (1,0)…

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Q: y=Arccos (x²)

A: The objective of the question is evaluate the second derivative of the given function.

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

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Q: Find L-1 ((₁+1)² (s+1)(s²-1)/

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Q: Determine the area bounded by f(x)=x²-x and x-axis. unit² B unit² Ⓒunt² D unit²

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

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

A: To find integrand the steps are as follows.

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

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Q: Initially 73 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

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Q: A car is travelling at the rate of 88 ft/sec when the brakes are applied. The car begins to…

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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: S Given dx, determine all value/values of P for which the improper inte хр A (-∞,1] B {0,1} C…

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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.…

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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: A If B C √ √ √(x + 1) dx (x+2)(x-1)² = √ [1+²+ = -1 + (-1²) x 2 (x−1)2 ]dx dx, the values of A & C…

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

A: Volume

Q: 4 [*(16-x²) dx

A: Using left reimann, approximate area is evaluated.

Q: Which of the following can be determined given A [²(f(x) + g(x) + h(x) dx 4 ® B √g(x) dx © (4f(x) +…

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Q: 3+cosh2x33+cosh2xsinh2x dx Evaluate the integral: e3+c (3e)3 + sinh2x A + C 2 + In3 (3e)3 + cosh2x B…

A: You must have idea of integration to solve it.

Q: 10 Σ (3n – 1): 125 n=1 10 Σ–1 (3) -1, 125 Σ (3n – 4): 125 10 Ο Σ(3n – 4): 125 Ο Ο O e Θ

A: Verify all the option   then find the sum.

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: for Which of the following can be determined given S √₁² f(x)dx = 5,³ g(x) dx = 7, and d Ⓒ [[²(f(x)…

A: ∫ab fx±gx dx =∫ab f(x) dx ±∫ab g(x) dx ∫ab kf(x) dx =k∫ab f(x) dx ; where , 'k' is an constant.

Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: QI/ sin x a) find dy/dx for the equation (y 1+cos x b) find f'(x) for the equation f(x) = sec x

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Q: Evaluate the double integral: A) 80 B) 30 C 60 D 40 √²² (3x² +9y²) dxdy 0 0

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

A: Please follow the next step.

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

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Q: The general solution of the equation (D4 +D²)y= -12 is Ay=C₁ + c₂x + c3cOSX + csinx - 6x² B y=C₁ +…

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Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 73°C, it…

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Q: The function is x z = y² What is 8²% dy² 2/21/23

A: Let's find second partial derivative of given function.

Q: y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: Solve the following y" - 3y' + 2y = 2x2 + ex + 2xex + 4e3x -

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Q: y=Arccos (x²)

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