The junior class has 50 students. Twenty-five students take French, 15 take Latin, and 10 take both. If a student is chosen at random from the class, what is the probability that the student chosen takes either French or Latin?

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Q: lim x →3 (x − 3) tan(9 — x²) sin²(2x - 6)

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Q: 59-62 Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d evi dt sin sin…

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Q: b. 36. Evaluate f(4x³ - 9x5 + 4x² - 6) dx. a. 32x7-45x + 8x + C 32x7 180x³ 4x9 C. b. 3 +8x + C…

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Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

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Q: IV. Do as indicated. 1. Let f(x): = where x = 1. 1 Find the equation of the tangent line to the…

A: Given equation f(x)=11+x2Differentiate…

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Q: 3. S 2 x²+a² x4 = _ (x² + a²) ³² 3a²x3 -dx = + c

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Q: 1o. 1 |x-3|dx

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Q: rπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

A: To evaluate the given definite integral.

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Q: 1. Identify the equations of all the linear asymptotes of f.

A: There are three different types of asymptotes for a function fx: (i) Horizontal asymptote: If we…

Q: V. Given: 2. Find f'(2), if it exists. el3z-61-2, f(x)=[2x - 5], √x²-9, if x ≤2 if 2 3

A: Solution is given below:

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Q: Using mathematical induction. Prove that Ž {i= n(n+1) WHEN 12 1 2

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: We have to integrate the given function for the given limits

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A: This is a problem related to integration. Based on the concept of partial fraction decomposition we…

Q: Select the conic section represented by the equation. 4x 2 - 25y 2 - 8x - 100y - 196 = 0. line…

A: We can answer the question as below.

Q: Integrate the following functions f(x₁y) = (x-1) =x over the given regions y=x²

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Q: d an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (4,…

A: Given; Points- (0,0,0),(4,0,6),(-4,-1,8)

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Q: 1. 2. 3. 4. 5. Stan² z dr cot cot2 r dr COS I da sin² x 2 COST da sin r 1₁ sin a cos² x + z] dz 6.…

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Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: Find an equation of the plane with the given characteristics. The plane passes through the point (1,…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Ex. (10) Sol Solve y"-2y' + 2y = 2x+3

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Q: 61. det t sectdt d 62. du Jo Ix/dx 0 px [Hint: Use Definition 5.5.3(b).]

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Q: xg x9-₂x = 1 4

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Q: limx→→∞ √1-x+2x+7 2 9x +5 - 3x

A: limit.

Q: Find the volume generated by revolving the given bounded plane area about the line. Use shell…

A: Volume

Q: Method A: Method B: Replacing cosa by 1-sina. Replacing sin by 1- cos². Replacing seca by 1 + tan²…

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Q: IV. Do as indicated. 1. Let f(x)= where z = 1. 1 ²+1 Find the equation of the tangent line to the…

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Q: Determine which of the vectors is (are) parallel to z. Use a graphing utility to confirm your…

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Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: Bernoulli Equations: 1. (x² + y²)dx - xydy = 0

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Q: Integration of Algebraic Functions By trigonometric Substitution dx 6. S x²√4-x² dx 7. S- √81+x² X…

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Q: Let f(x) = 3x + 6 x + 7 Find: 1) the domain in interval notation Note: Use -00 foroo, oo for oo, U…

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Q: 3. Suppose that the revenue in selling a tables is equal to 200x -0.25x² dollars, and producing a…

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Q: 33. (a) L²₁ let - 11 dx r3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Ex. (9) Solve 3y"-2y' + y = 4x+2

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Q: Y 4- y = f'(x) 3 -3 -1 (1,0) 2 3 -4 (-3,0) W (0,-0.5) (2,-0.5) (3,-2) -1,-2) -3- (-1,-3) (4, -3) 2 I

A: Observe the graph and answer the question.  Concept:  h'(x) = 0  : h(x) has local maxima Or minima…

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

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Q: V. Given: 2. Find f'(2), if it exists. f(x) = el32-61-2, [2x - 5], √x²-9, if x 3 14

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate the following limit using L'Hospital's rule. lim (e⁹x x⇒0+ 6x) ( ) +

A: Using LHospital Rule , limit is evaluated.

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = − 1 − 2x, dv = f(x)dx, then the…

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