In Exercises 1-10, factor out the greatest common factor. 2. 16x - 24 1. 18r + 27 3. 3x + 6x 5. 9x* – 18r + 27x 7. x(x + 5) + 3(x + 5) 9. x(x - 3) + 12(x - 3) 4. 4x2 - 8x 6. 6x* - 18x + 12x? 8. x(2r + 1) + 4(2x + 1) 10. x(2x + 5) + 17(2x + 5)

Q: The integral in this exercise converges. Evaluate the integral without using a table. 2 S 2 S 0 V…

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Q: Evaluate Hint: Use differentiation to show that n=1 (1 – x)-2 = nx"-! (for |x| < 1)

A: We have to show that 1-x-2=∑n=1∞nxn-1

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Q: f(x) = Use the limit definition of the derivative to find (1) ƒ'(-3) = (ii) ƒ'(-1) = (iii) f'(2) =…

A: derivative of  fx=1x-1, using limit definition

Q: -5 ƒ(x) = 3x + ½, find ƒ'(-5), using the definition of derivative. f'(-5) is the limit as of the…

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Q: Express g(x) + h(x) as a rational function, where g(x) = 2x and h(x) = 3 x - 1.

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A: Slope of curve is derivative of this curve

Q: Use the properties of limits to help decide whether limit exists. If a limit exists, find its value.

A: Given limit, limx→10 x2-100x-10

Q: Q7: Show all your work in this problem. Consider the infinite series ∞ k - 1 2k + 1 k=2 (c) Write…

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Q: Determine whether the following statement is true or false, and explain why. eln(- 2) = -2

A: Given data:- eln-2=-2

Q: Consider the graph of f(x), the derivative of f(x). Find each of the following: You must use…

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Q: Find the interest rate needed for $6000 to grow to $8000 in 3 years with continuous compounding.

A: Given data:- Rate of interest = r Final amount, A=$8000 Principle amount, P=$6000 Time, n=3 year

Q: Given the following limit, select all statements that must be true. lim h→0 f(−3+ h) − f(−3) h = 9

A: Given: Let us assume x=-3+h⇒h=x+3. So,

Q: Let us summarize continuity of a function at x=a (where 'a' is a value in the domain of the…

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Q: To find the values of x at which x3 - 2x + 1 = 0?

A: You can get one root by hit and trial and other roots by solving the quadratic equation obtained by…

Q: Determine whether the following statement is true or false, and explain why. The function ƒ(x) = 3x2…

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Q: How to find the derivative using quotient rule for: f(x)= 7x+7 / 6x+3 f’(x)= f’(1)= Plz explain the…

A: Topic:- application of derivatives

Q: Find the exact length of the curve. x = 1 + 9t2,    y = 7 + 6t3,    0 ≤ t ≤ 4

A: Length of curve=∫abdxdt2+dydt2dt, provided a≤t≤b

Q: Consider the graph of f(x), the derivative of f(x). Find each of the following: You must use…

A: We know function fx increasing when f'x&gt;0and function fx decreasing when f'x&lt;0function concave…

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Q: 1(x, y, z) = ln(2x + 4y + z²), at the point u = (−1,1,0), in the direction of the unit vector…

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Q: Explain the Bessel function.

A: Concept Used: Bessel function General form of the Bessel function is: y(x)=AJn(x)+BYn(x)

Q: 2. Find the general equation of the circle passing through(1,1), (−2,3) and (3,4).

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Q: Solve cos(x) = -0.88 on 0 ≤ x < 2π There are two solutions, A and B, with A< B A = B = Give your…

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Q: Evaluate. (5z – 4)sin(4x – 9) dx = dz

A: Integration by parts ∫uv=u∫v-∫u'∫v   whrer  u and v are functions.

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Q: For Exercises 31–44, graph the equations by plotting points. (See Examples 4–5) 31. у 3 х 32. у = x…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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Q: If sin t and is in quadrant I, find the exact value of sin (2 t), cos (2 t), and tan (2 t)…

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

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Q: D. Solve the Bernoulli's DE: 4y³¹ (x² + 4 + 4xy¹ = (x² + 4)²

A: The  given differential equation is; 4y3(x2+4)dy/dx + 4xy4 =(x2+4)2.

Q: Write an equation describing the relationship of the given variables. y varies inversely as the cube…

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Q: Explain how to convert from scientific to decimal notation and give an example.

A: Let's consider the two numbers 91200 and 0.000912.The scientific notation of these two numbers is…

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Q: Let y y' = = = ex -2 sin³ (t) dt. Use the Fundamental Theorem of Calculus to find y'. ▶

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Q: A plate in the form of an isosceles triangle with base 10 ft and altitude 4 ft is submerged…

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Q: EXAMPLE 3 Writing an Equation of a Circle in Standard Form Write the equation of the circle in…

A: The standard form of the equation of circle with center h, k and radius 'a' is as follows:…

Q: 2-4 +4² +16 Give your answer as an integer or a fraction. If the limit does not exist, type DNE.…

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Q: Use the substitution method to integrate the following. Do not write "+ C", as it is already…

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Q: The symbol V is used to denote the nonnegative, or square root of a number.

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Q: Solve equation. If necessary, round each answer to the nearest thousandth. log3(2x + 5) = 5

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Q: Consider the function 7x y² At a point (a, 3) the derivative in the direction (6,5) is 3√61.…

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Q: What can you tell about the graph of a polynomial function of degree n before you plot any points?

A: A polynomial is said to be of degree n if f(x)=axn+bxn-1+...+cx+dwhere a,b,...,c,d ∈ℂ=set of all…

Q: Given f(x)= x - 4x³ +10. a) b) d) Find the intervals of increase and decrease. Find the local…

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Q: 3. Show that y(x) differential equation C₁e²c₂e-3, where c₁ and ₂ are constants, is a solution of…

A: #Q3

Q: EXAMPLE 1 Writing an Equation of a Circle in Standard Form a. Write the standard form of an equation…

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Q: Solve the following initial-value problem: y' + (tan x)y=cos²x; y(0) = -1 O O y = (cos x) (sin .x -…

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Q: For the function f(x) = -5²+1, compute the limit lim h→0 f(x+h)-f(x) h

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Q: 8. Is the point (2, –7) on the circle defined by (x + 6) + (y + 1) = 100?

A: Given the equation of a circle, x+62+(y+1)2=100                   ...(1)

Q: x³ y" + xy' - y = 0 [ Hint: x = e¹, ln x = t; x(dy/dx) = dy/dt; x²(d²y/dx²) x³(d³y/dx³) = (d²y/dt2)…

A: The given differential equation, x3y'''+xy'-y=0 We have to find the general solution of the…