Problem Solving: Prob. 1 A block of mass M = 10 kg is sitting on a surface inclined at angle 0 = 45°. Given that the coefficient of static friction is µ = 0.5 between block and surface, what is the minimum force F necessary to prevent slipping? What is the maximum force F that can be exerted without causing the block to slip? F M

Q: Evaluate the triple integral: 3 ₂2 0 (x+y+z)dydxdz

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

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Q: Solve the integral: S- ® in/1+x A) an 1 B_5n/1+x' 5 6 1 √√√x + x + C + C c dx

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Q: luating√√9-x² dx using trigonometric substitution will lead to: **/2 sin²0d0 3 of th 9[*/ cos²0de…

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Q: Find the volume of solid generated by revolving the region bounded by f(x)= x² + 1and g(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: Solve the integral: Seln(2x² + 3x −4)³ (4x + 3)dx eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) A + C…

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

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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 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: 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: An equation of a hyperbola is given. (x+3)²-(y - 3)² - 1 9 16 (a) Find the center, vertices, foci,…

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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: 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: [² -dx, determine all value/values of P for which the improper integral Given converges? (A) {0,1}…

A: The integral is ∫1∞ 1xpdx

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

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

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Q: A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward the pole with a…

A: Given problem:- A street light is at the top of a 10 ft tall pole. A woman 5.75 ft tall walks toward…

Q: How many antiderivatives does a function of the form f(x) = x^ have when n0? (A) 1 B) none (C)…

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Q: y= 3 Arcsec 3x

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Q: Which integral below gives the volume of the solid of revolution obtained by rotating the bounded…

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Q: Evaluate the triple integral: A) 12 B) 24 C) 6 D) 18 3 2 (x+y+z)dydxdz

A: To evaluate the given triple integral.

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

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Q: Given the integral sec (x - 1) tanª (x - 1)dx, which of the following equations will be useful for…

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Q: Given the integral sec (x - 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: Let's find useful formula for evaluation of integration.

Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.

Q: Question 15 Evaluate the double integral: (A) 40 B) 80 C) 60 (D) 30 ²² 6) (3x² +9y²) dxdy

A: we can find the double integral.

Q: y = Arctan ( 2+x 1-2x

A: The derivative are

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

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

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Q: +3x-4)³ (4x+3)dx + C Solve the integral: Seln(2x²+3 (2x²+3x+4)*(4) A 3 (2x²+3x+4)4 4 eln(2x²+3x-4)³…

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Q: X √√√3/2 x² Solve the integral: A 6√√x +C 3√√x² (B - + C 6 Ⓒ3√√√x² +C с √x (D 3 dx

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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…

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

A: The volume of the solid is 63π unit3

Q: (A) B (C) (D) **/2 18 [*/ ces **/2 cos²0d0 18 sin²0d0 cos²0d0 0 of the 0 **/2 $ cos²0d0

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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 B if the 0 1 0 e dx is

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Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: We have to find out derivative

Q: Find d2y/dx2 for y2 + 2y = 2x + 1

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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: Evaluate the improper integral A diverges B) 0 с 3 Alu 112²232/3 dx 4

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Q: Determine the integral: [x²cosxdx A x²sinx+2xcosx-2sinx + C (B) x²sinx-2xcosx + 2sinx + C…

A: On solving this we will get

Q: dx using miscellaneous substitution will yield to secx + 1 nsforming - S 1+2 / dz √²-22² dz 1+z²…

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Q: Evaluate the improper integral A 0 B 2 (C) с D) diverges 3 4 12330² dx

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A may vary depending on…

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