х2 — 4х + 1 lim Зх — 5

Q: Derivative rules Compute the following derivative.

A: ddtt2(i⏜+2i⏜-2t k⏜.(eti⏜+2 et j⏜-3 e-tk⏜))

Q: dy d {-3xy} in terms of x , y , and dx y is a differentiable function of x . Write dx

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Q: Binomial series Write out the first three terms of the Maclaurin series for the following functions.

A: fx=1+x2-3 Differentiating with respect to x, we get f/x=-31+x2-4·ddx1+x2=-31+x2-40+12=-321+x2-4 Agai...

Q: Our goal is to use function notation to represent the total fuel cost, in terms of the distance (in ...

A: Given that we need to represent volume using function notation in terms of the  distance d of a trip...

Q: Evaluate lim f(x) and lim f(x) for the rational function. Then give the horizontal asymptote of f (i...

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Q: Find the first partial derivatives of the function. f(x, y) = x^y³ + 8x5y 4,3 %3D

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Q: Consider the geometric sequence: -5, 10, -20, 40, ........Solve, Find the sum of the first ten terms...

A: The geometric sequence is -5, 10, -20, 40, ...   To find: Sum of the first ten terms of the sequence

Q: Find the second derivative #59

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Q: Simplify : (2/7)0-32-2/5

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Q: The question is attached

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Q: I need help with question 1 of the atachment thank you

A: Given that the domain of the graph is (-4,∞) limx->-4+f(x)=3 when x approaches from the right of ...

Q: Find the derivative of the function. f (x) = 1/ ( 1+ x 2  )

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Q: Solve the initial value problems for r as a vectorfunction of t. Differential equation: dr/dt = -t i...

A: given: drdt=-ti-tj-tk r(0)=i+2j+3k

Q: Solve the following IVP using Laplace Transform. (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii) y′′+3y′+2y...

A: given Initial Value Problem is, (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii) y′′+3y′+2y=e^(-t), y(0)=0 y...

Q: Consider f(x) V2x – 7 g(x) Use interval notation to state the domain of the following functions: and...

A: Hey, since there are multiple questions posted, we will answer first three question. If you want any...

Q: find the derivative. p=(sec q + csc q)/csc q

A: Given function  p=secq+cscqcscq

Q: Integration review Evaluate the following integrals.

A: We have to evaluate I=∫lnw-17lnwwdw Let substitute  u=lnw-1 Differentiating both sides with respect ...

Q: Solve the exponential equation 8x = 12,143. Where necessary, express the solution set in terms of na...

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Q: Find the first partial derivatives of the function. z = (7x + 8y)7 dz %3D dx %3D dy

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Q: Find the first partial derivatives of the function. f(x, t) = /x In(t) %D fx(x, t) = %3D fe(x, t) = ...

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Q: . The profit P from selling x units of a product is given by        P = 560x − 0.2x2. The sales are ...

A: The profit P from selling x units of a product is given by :         P=560x-0.2x2 Now, The sales are...

Q: Fill in the blank/s:

A: given that limx→af(x)=L.

Q: Find a fundamental matrix of the systems in, then apply Eq. mentioned in the Attachement, to find a ...

A: We have given system of equation X'=3-111X,            X0=10      

Q: Calculate the derivative #65

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Q: Q-1: Integrate each of the following without using trigonometric substitutions (a) S: cos(x) xp- sin...

A: Integrating each of the following without using trigonometric substitutions

Q: Find r'(t) and antiderivative[r(t)]dt of: a. r(t) = <2tan(t), -sec(t), sin2(t)> b. r(t) = te3t...

A: (a) Obtain the derivative of r as shown below: r't=ddt2tant,ddt-sect,ddtsin2t     =2ddttant,-ddtsect...

Q: Find the derivative of the following function using the rules of differentiation: g(x) 3xv1+ x?

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Q: Use the properties of logarithms to expand the logarithmic expression.          ln xy/z

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Q: Find the vertex, focus, and directrix of the parabola. (x + 1)2 = 12(y − 2)

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Q: Let f(x) = 5x +7 and g(x) x2 + 2x – 63 • You must combine all like terms before you submit your answ...

A:   (a) To find: The composition of the function fogx. Given information: The functions are gx=1x2+2x-...

Q: Solve the polynomial inequality and graph the solution set on a real number line. Express the soluti...

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Q: Find the first partial derivatives of the function. z = (7x + 8y) az !! ax %3! ду

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Q: Find the horizontal asymptote, if any, of the graph of the rational function. 14x h(x)%D 4x2 +9 Sele...

A: The given function is hx=14x34x2+9.  

Q: Find the limit

A: The given expression limx→013+x-13x

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter an...

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Q: Find an equation of the tangent plane to the given surface at the specified point. z= 2(x = 1)² + 6(...

A: Given: The equation of surface is z=2(x-1)2+6y+32+1, and the given point is 3,-2,15 To find: The equ...

Q: (In =)"dz = z(lnz)" – n (In =)*- da Use integration by parts to establish the reduction formula: %3D...

A: Formula given is  ∫(lnx)ndx=x(lnx)n-n∫(lnx)n-1dx Integration by parts formula is  ∫udv=uv-∫vdu we ca...

Q: Use intercepts to graph equation. 6x - 9y - 18 = 0

A: 6x-9y-18=0. To find x-intercept, put y = 0 in the given equation, we get 6x-90-18=0⇒6x=18⇒x=3 Theref...

Q: If z = x2 - xy + 2y2 and (x, y) changes from (2, -1) to (2.03, -0.95), compare the values of Az and ...

A: The function z = x2 – xy + 2y2 and (x, y) changes from (2, -1) to (2.03, -0.95), we have to compare ...

Q: Factor completely, or state that the polynomial is prime. 12x2 y - 27y - 4x2 + 9

A: According to the question, we have to factorise the polynomial 12 x2y-27y-4x2+9. Factoring is a proc...

Q: Using the second derivative test, find whether the function: x^3-9x^2-48x+52, has a local minimum or...

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Q: Find the exponential function y = Cekt that passes through the two given points.

A: Given that, y=Cekt             ...(1)

Q: find dy/dx by implicit differentiation x2y2 = 1

A: According to the question, we have to find the differentiate x2y2=1 by implict differentiation, Impl...

Q: 1. The graph of y=cscx has zeroes at? ( does it not cross the x-axis?) 2. What is the equation for t...

A: The graph of csc(x) never meets the x-axis. Since csc(x) = 1/Sin(x) And the magnitude of Sin(x) vari...

Q: (1) Suppose you lift a stone that has a mass of 5.2 kilograms off the floor onto a shelf that is 1 m...

A:  Definition used-   Work done                                         w= F·d                        ...

Q: In Exercises 39 and 40, use the surface integral in Stokes' Theorem to find the circulation of the f...

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.