5. Find the area of the region bounded by y=x² - 6x +5 and the x-axis. 125 (a) A= square units 3 (b) A= square units (c) A = 3 125 (d) A= 32 3 3 32 square units square units

Q: 2) Find the radian measure of angle 0 in the figure below. 22.5. a) O 2.25 radians b) O 4.5 radians…

A: we know that arc 2πR =2π radians

Q: Problem 1. Solve these integrals using substitution (a) x(x-2)³ dx, (b) text² di dt.

A: The given integrals:a∫xx-25dxb∫te3t2dtWe will solve them using substitution.

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Q: Find the area of the region enclosed by the graphs of the polar curves given by 8/4, 0 = 0 and r cos…

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Q: 1. Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2. 2. Find the length of the r(t)= , 1 ≤ t ≤ 5…

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Q: Use algebra to evaluate the following limits. 3x4 - 5x² x² 2x² - 2x-12 a) lim x-0 b) lim x+3 x²-9

A: Here we will use basic limit laws and algebra to find the limits.

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A: Given, ∫0π4141-cos12xdx

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Q: 3. Integral xdx 10x -234

A: We will use substitute method to solve this integral.

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Q: Classroom activity 9.1 the monthly income earned by each of the following workers paid by the hour…

A: We have to determine the monthly income.

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Q: find the explicit solution of y' +xy = x√ y

A: This is a basic differential equation problem

Q: What is the area under the graph of y = 2 54-3-2-1 O O N/W 13 2 15 2 ਜਾਨ , -2+ -3 4 1 2 3 4 5 X on…

A: The region is bounded by the graph y=2-x on the interval -2,1

Q: Find (f+g)(x) and identify the graph of f+g. f(x)=x² and g(x) = 5 Part: 0/2 Part 1 of 2 (f+g)(x) =…

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

Q: Using the Inverse Function Theorem, what is (-1) (8) given that (x) = √6x-2? Note that (11)= 8. (Do…

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Q: 73. an = (2n + 2)! (2n-1)!

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Q: What is the area of the region in the first quadrant bounded above by y = -2x + 8 and below by y =…

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Q: The base of a three-dimensional figure is bound by the line X = √y on the interval [1, 4]. Vertical…

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Q: I. Integration by Parts. Evaluate the following integrals. [cot-¹ a 1. rdr

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Q: The fourth left-endpoint in a partition of [0, 3] with Ax = 0.5 is

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Q: III. Partial Fraction Decomposition: Evaluate the following integrals using partial fra sition. 1.…

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Q: S(x + ex+1) dx 0 2. Sx5¹2 (x³ + x² - 7) dx 0 2x + 1 3. dx 2 0 e

A: Topic = Integration

Q: Solve equation: 4 sin x + 3 cos x = 5

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Q: Use the graph of f(x) to determine the following limits. The domain of f(x) is x E R. If the limit…

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Q: X f(x) g(x) -2 5 1 -1 2 3 0 4 1 -2 2 -4 -3 -6 -1 f'(x) -4 -2 1 5 -5 g'(x) -1 3 -3 4 2

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Q: Use the formula for the area of a trapezoid to evaluate √₂² (2x- 2 (2x + 3) dx.

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Q: Graph the linear inequality. 4x-y < 4 CIB Use the graphing tool on the right to graph the…

A: Here we will draw inequality,

Q: Two matrices A and B are multiplied to get AB if O both are rectangular both have same order number…

A: If A and B are two matrix then matrix AB is defined only when  (A) A and B are of same order (B) The…

Q: Show that there are no tangents to the curve f(x) = 6x3 + 2x2 that have a slope of -5.   Please…

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Q: A region bounded by f(x) 6 5 4 3 Find the volume of the solid formed by revolving the region about…

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Q: Find the general solution of the following differential equation. 25y" +10y + y = 0 NOTE: Use c₁ and…

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Q: 15. y = (In x) Inz

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Q: Find the general solution of the given second-order differential equation. 30y" 19y' 5y = 0 -…

A: See the details solution in below

Q: Sketch left-endpoint and right-endpoint approximations for f(x) = on [1,2]; Approximate the area…

A: fx=1x on 1,2, n=4

Q: (b) Use L'Hopital's Rule to find the following limits: e-1 x (i) limx→0 (ii). lim-0 x-y fl (x > 0, y…

A:

Q: (5) f(x) = cos (5 - 2x) (7) f(x): = cos (√x³ + 1) (9) f(x) = cot (x5) (6) f(x) = cos (4x7 + 3) (8)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: Evaluate x/10 Than S 11√1+ cos 10x dx. 0

A: We know that integration of cosx is sinx +C . And trigonometry relation is - Cos2x = cos2x - sin2x =…

Q: If f³ f (x) dx = 6 and ſ ƒ(x)dx = 4, then ſ5 (3 + 2ƒ(x))dx : = 35 10 23 20

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Q: consider the function f, such that f(x) = (ax + 3) * e*. If the slope of the tangent line to the…

A: Topic = Derivative

Q: Find the general solution of the following differential equation. y" + 5y +6y=0 NOTE: Use c₁ and ca…

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Q: Let f be a function with continuous second partial derivatives and define: z = f (2x³y - y₁y³) if…

A: z= f(2x3y-y,y5) ,  u= 2x3y-y, w= y5   And zy= (2x3-1)fu+5y4fw  Find zyx

Q: = [₁²₁ Use the Fundamental Theorem of Calculus, Part 1 to find the derivative of g (r) : = x² + 4dx.

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Q: 6. 7. 3+6s+45²-25³ s² (s² + 3) 26-5²- s(s² + 4s+13) [2+1+√√3 sin √√3t-4 cos √√3t] 2 [2-3e-2t cos 3t…

A: To find the inverse laplace of the following.6 3+6s+4s2-2s3s2s2+37 26-s2ss2+4s+13

Q: 15. integral sin 4x cos 4xdx

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Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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