Given functions g(x)=√x+14 and f(x)=z-6, state the domains of the following functions using interval notation. Domain of g(x) f(x) Domain of g(f(x)) Domain of f(g(x)) :| :

Q: Find the x-values (if any) at which fis not continuous. Which of the discontinuities are removable?…

A: Using property of rational function,

Q: Solve: 2|z-21 +4>7 The answer has form: Ox B OA<x<B Where A- and B

A: We have to find the value of A and B

Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = y =…

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Q: Problem 3

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Q: r(t) = (t, In(t), √t), to = 1 e the equations for the line to approximate r(to + 0.1). to + 0.1) =

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Q: Solve the following differential equations of y" + 6y' + 5y = 10 sin (2x)

A: The given differential equation is  y''+6y'+5y=10sin(2x).

Q: Find the exact value of cos(195°) using the fact that 195⁰ = cos(195⁰) = 225° -30°.

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Q: Write the given (total) area as an integral.  • The area above the x − axis and below y = 4x− x²…

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Q: More on Areas. Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence…

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Q: (D² – D − 2)y - COS X

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +9 1 = lim t→+∞ (?, ?) 7t² + 8' 4t,

A: Given problem:-

Q: Set up the definite integral required to find the area of the region between the graph of y = 19 -…

A: area between curve

Q: For F(x, y, z) = (x + yz) i + (y + xz)j + (z + xy) k, find: (a) the curl (b) the divergence

A: To find curl F and div F

Q: Theorem (Two-Path Test). Let f be a function defined by z = =f(x, y). If f has different. limits as…

A: limx, y→0, 0x2yx2+y2

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Q: Evaluate: lim (cos x)=¹2 X x → 0

A: Since the numerator is positive and the denominator x^2 approaches zero and is greater than zero for…

Q: Use the rules of differentiation to find the derivative of the function. y=9x². + 7 sin x

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Q: Suppose that f(x) and g(x) are given by the power series f(x) = 6+7x+7x² + 4x³ +….. and g(x) =…

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Q: Prove the identity. (secx+1) (secx-1)=tan ²x Note that each Statement must be based on a Rule chosen…

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Q: Use the following binomial series formula to obtain the MacLaurin series for ∞ (a) (1+z) k=0 (b) √ 1…

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Q: Solve xy = 8y - 3x, y(1) = −1. (a) Identify the integrating factor, a(x). a(x) = (b) Find the…

A: xy'=8y-3x

Q: Prove the identity. COS X 1-sin x 1+ sin x COS X Note that each Statement must be based on a Rule…

A: Solution )  cos x / ( 1 - sin x ) Multiply cos x in numerator and denominator =cos x × cos x /  […

Q: On Integral of Trigonometric Functions: Determine the integral of the ff. functions. 3. sec 2 (3x +…

A: To find the integration of Functions: As per Bartleby guidelines we are supposed to answer only…

Q: Find dy. Do not simplify your dx answers cashy (x² + + 7) = x curt y² 1. COS -241

A: As per the instruction, we will be answering only the first question. For (1),…

Q: interval of convergence = 0

A: Follow the procedure given below.

Q: Use the Ay dy 1

A: Use the information to find and compare ∆y and dy .     y=x4+2 , x=-3  and  ∆x=dx=0.01

Q: Determine the sum of the following series. 31 10 Σ(1)

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Q: Describe the graph of the equation. r = 7costi 14 sin tj + k O An ellipse in the plane x = 1, center…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

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Q: A tank is full of water. Find the work required to pump the water out of the spout. Use the fact…

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Q: Given the function f(x) = -√√x + √³, find f'(6). Express your answer as a single fraction in…

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Q: In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the…

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Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: r = 12 sin 18ti + 12 cos 18tj

A: Given :

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

A: Let's find.

Q: Find a power series representation for the function. (Give your power series representation centered…

A: Given:        f(x) = 1/ ( 5 + x )

Q: ind r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). r(t) = 2t²i - 2tj + 5t³k (a) r'(t) (b) r"(t) (c)…

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Q: Cheyenne, Wyoming, has a latitude of 41° N. At this latitude, the number of hours of daylight D can…

A: Given :  D = 2.914 sin(0.017t 1.321) + 12.134

Q: Find all solutions of the equation in the interval [0, 27). 2cos’x– cosx−1=0 Write your answer in…

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Q: 12. Prove that the intersection of any family of normal subgroups of a group (G, *) is again normal…

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Q: Which of the following is the derivative of (x³ + 1)(x² + 2x)? 3x²(x² + 2x) + (x³ + 1)(2x + 2) 3x²…

A: This question is based on product rule of differentiation.

Q: Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers…

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Q: Find the limit of the trigonometric fur lim cos (5) 248

A: answer is in next step

Q: I need all the integrals of the trigonometric ratios

A: ∫sin x=-cos x+C∫cos x=sin x+C∫tan x =-ln|cosx|+C

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Find the volume of the ellipsoid x² + y² + 10z² = 49.

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

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Q: An ellipse of equation 4x²+2y²=k the distance between its foci 3√2 Find the value of k

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Q: A table of values of an increasing function fis shown. X 10 14 18 22 26 30 f(x) -11 -5 -2 1 5 Use…

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Q: Write the Taylor series for f(x) = sin(x) at x = Find the first five coefficients. Co= C1= C2= C3=…

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