Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

Q: Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist,…

A: f(x)=(x+5)23  f'(x)=23(x+5)-13  f'(x)=23 (x+5)3Let's understand f'(x) as a different…

Q: O A- 32°, B - 59°, C = 89° %3D

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Q: Using decomposition into partial fractions, 3x2 + 2 dx J x(x2 + 2) is equal to

A: The objective of the question is evaluate the indefinite integral using decomposition of partial…

Q: The functiion?n f(x)=/x) is odd or even?

A: Explanation of the answer is as follows

Q: What is the solution of D.E y"- 3y' = -2cos(2x) when solved using the method of undetermined…

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Q: 10. Create examples of functions (and also justify why it works for each): a) Continuous and…

A: As per bartleby guidelines we are supposed to answer only 3 subparts of a particular question. This…

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

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Q: s required to repay a loan that matured to $4,550 on August 14, 2015. ne realized that he could…

A: Topic:- simple interest

Q: 12 Indicate a general rule for the nth term of this sequence. 6m, 3m, 0, -3m, -6m, . . . a n =…

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Q: For some constant a, the following improper integral | (x2 – 1)e2xdx converges to converges to e2a…

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Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

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Q: Su(u² + 3) du

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Q: 5.1. Find the area enclosed by r = V cos(0). (Ignore the r= 2 cos(0) for this part of the problem.)…

A: 5.1) To find the area bounded by the curve r=cosθ

Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: Without evaluating the constants, the partial fraction decomposition for 5x? – 3 f(x) %3D (x3 -…

A: Given :5x2-3(x3-4x)(x2+3x+2)(x2+1)

Q: 7. Determine the integral| 2+1

A: The given integral,    ∫x dxx2+1

Q: The following are the critical points for the function f (x, y) = x³ Зху + уз - State what…

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x -…

A: Given that f'(x)=x-12x+2

Q: 12. Let y = 4x-4x+3. %3D (a) Find the equation of the tangent line to the graph of the function at…

A: Solve the following

Q: The average rate of change of y with respect to x over the interval [0, 3] for the function y = 3x…

A: The function y=3x+2 over the interval 0,3

Q: Question 2 - a) [i- :- :]: Explain why the following series (-1)" 1+ n3/2 n=1 is Alternating. ]: Use…

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Q: Find the area of the region enclosed by the graphs of x + (y – 1)² = 1 and 2x = -y?.

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Q: 4.) f(x) = etinlx)+cos (x) 2+4x+4 5.) (x) = = 6.) S(x) = +r-s)(ar-7) 622-131+7

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

A: We need to find dimension of the garden.

Q: Graph the polar equation. r-4 cos 0 1444 1234.

A: To graph the given polar equation.r=4 cos θ

Q: From Rogawski ET 2e section 10.7, exercise 58. Find the first four non-zero terms of the Maclaurin…

A: Given problem:-

Q: С. O c. v = 2 m/s

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Q: (b) Find the values of a andb so that the function f(x) = x2 + ax +b has a local maximum at the…

A: We have to find the value of a and b

Q: da a 2 +10a+25a 2

A: Given,  ∫ 1a32+10a+25a12da

Q: 5. The partial graph of y = logb x passes through the point P (2,0.5) and Q (a , 2). The value of a…

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Q: Sx² sec2 x³ dx

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Q: ANOTHER A baseball team plays in a stadium that holds 52,000 spectators. With ticket prices at $10,…

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Q: Jx In x dx S x

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Q: Evaluate the difference quotient fla+ h) - fla) for the function f(x) = 6x. 1

A: Given  f(x) = 6x  We need to find the difference quotient  f(a+h) -f(a)h…

Q: On the circle x² + y² = r², find y". r2 A. y" C. y" = y - x3 E. None of these -x² - y2 В. у" D. y" :…

A:

Q: Problem #2: Differentiate f(x) = [(2x3 – 8)(5x² – 3x – 9)]° and solve f'(2). Solution: Reason:

A: The given function,      f(x)=2x3-85x2-3x-93

Q: b. In the interval (0,5), f is not differentiable at x = (Use a comma to separate answers as…

A: Function is not continuous at those point where the graph of the function has missing points in…

Q: Evaluate the integral x(x® –4) dx 1. O 1 10 (xº – 4)" +C 50 O 1 +C 60 10 +C 10 x° ( x7 -4x +C 6 7

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Q: Use a right triangle to write the expression as an algebraic expression. Assume that x is positive…

A: see below the answer and calculation

Q: A 17-ft ladder is leaning against a wall. The foot of this ladder is sliding away at the rate of…

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Q: Complete the following steps for the given function, interval, and value of n. a. Sketch the graph…

A: Given, f(x)= 2x²+1 [1,6] n= 5

Q: The polynomial of degree 4, P(x), has a root of multiplicity 2 at a = 2 and roots of multiplicity 1…

A: Root of multiplicity is defined as the number of times each roots appears.

Q: Evaluate the summation (2i - 1)? - i=1 155 162 165

A: Topic = Algebra

Q: Question 11 Find the area of the triangle having the given measurements. Round to the nearest square…

A: Given    Angle C = 100°   Side a = 3 yards    Side b = 8 yards

Q: (9) Verify the following (a) cos e + sin 0 tan e = sec e %3D

A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

Q: 1 The resulting 8. 6. The graph of y = log, x is horizontally stretched about the y axis by a factor…

A: Given , a graph y=log2x x is horizontally stretched about y axis by factor of 18 we need to find the…

Q: O O O O For the differential equation (x2-4)y" + (x-2)y'+ 2y 0, a regular singular point is: O x-4…

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Q: Evaluate the limits lim x² + 3x- 4. x→-1 -6 -7 -2

A: We can find the limit as below.

Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)*dx xp. 2. S cos 3x dx

A: LetI=∫cosx+sinx2dxI=∫cosx+2sinxcosx+sin2xdxApply the Sum RuleI=∫cosxdx+∫…

Q: Compute the partial derivatives: 5x dz dz

A: