Use the e-8 definition of a limit to compute the value of the following limits: 1. lim -3x+1 3

Q: Evaluate the expression without using a calculator. In e 6 In e 6 =

A: Here we have to find out the value of  ln (e)^6

Q: Let C be a plane curve given by the parametric equations x = f(t), y = g(t), a ≤t≤b. Suppose that C…

A: Let a curve C be parametrized by x= f(t) and y = g(t),

Q: Consider the function f(x) = x² - 6x +8 x-1 a. Find the first derivative. f'(x): b. List any…

A: see below the answer and calculation As per Bertleby guideline I have to solve only first three…

Q: Find the limit. lim (1)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at…

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Q: Graph f(x)=3* and g(x) = log 3x in the same rectangular coordinate system.

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Q: Find the indicated derivative. 1 - 2x² x4 - 2x² + 6 dy dx || dy dx for y =

A: I am attaching image so that you understand each and every step.

Q: Write the integral as a sum of integrals without absolute values and evaluate: ƒ³ |x³| dx : =

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Q: Evaluate the definite integral 5 2 X dx

A: Given query is to find the integral.

Q: Given the implicit curve arctan(x² − y) + sin(2x + y) = xy + 8, find the tangent line at (-2,4).

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Q: Letū= (-2,37₁ v = (-5,27 and W = (-2₁4) Find the vector X that statif statisfies in this X = 1…

A: See this solution in below.

Q: A tank with a capacity of 400 L is full of a mixture of water and chlorine with a concentration of…

A: Given A tank capacity is  400L , chlorine with a concentration of  0.05g/L Fresh water enters at…

Q: Find the following limit. lim cot (4x) 24

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Q: Find the arc length of f(x)=ln|x| over [1,3]. Round answer to two decimal places

A: We will find the required arc length.

Q: Use the e- definition of a limit to compute the value of the following limits: 1. 2. lim 2² – 5

A: We  will find the required  limit.

Q: If x is divisible by 5 or y is divisible by 5, then xy is divisible by 5.

A: Let x is divisible by 5. Then x=5u for some natural number u.

Q: 3. Given h(x) = 3 ln(1 + x²) + 8 arctan(x), find all x where h"(x) = 0.

A: Topic - inflection point of a function We are given h(x)=3ln(1+x2)+8arctan(x)we know…

Q: Find volume by revolving the given area about the y-axis using the shell method. Answer in terms of…

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Q: Find the indefinite integral. (Use C for the constant of integration.) (-8x7) dx |

A: Let A=∫e^-X^8(-8X^7)dX        →  ∫X^n=X^(n+1)n+1

Q: Assume that the relation x = √500+ 5y² defines y implicitly as a function of x. Determine y" as a…

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Q: Weekly sales of graphing calculators can be modeled by the equation s(t) = 10-te-t/20 where s is the…

A: Given a rate of change function for any physical quantity over a given period of time t, the total…

Q: Recently, a certain bank offered a 5-year CD that earns 2.02% compounded continuously. Use the given…

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Q: The vector in the opposite direction to ū= (2,4) and of half its length is

A: Given query is to find the Indicated vector.

Q: Given 4x - -3x-y-7√ √/5y+ 8z = 5, calculate Provide your answer below: dz dx

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Q: lim 8e +71-8 2e¹+3r-2

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Q: For y = 88√x, find dy, given x= 4 and Ax=dx=0.22. dy= (Simplify your answer.)

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Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the…

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Q: Given 2y-√x-z+2√-5y-4z = -5, calculate Provide your answer below: || dz dx

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Q: y" + y = 2, y(0) = 4, y' (0) = 3 (A) y = 2 sint + 3 cos

A: given y'' + y = 2 D2y + y = 2(D2 + 1 ) = 2 for complementary solution D2 + 1 =0D = ±iD = 0…

Q: Find the normal vector to the level curve f(x, y) = c at P. f(x, y) = 6 - 5x - 4y c = 6, P(0, 0)…

A: Find the normal vector to the level curve f(x, y) = c at P. given f(x, y) = 6-5x-4y and C = 6, P(0,…

Q: Unit Find the vector = (-3,₁27, in the direction opposite to V

A: Topic = Vector

Q: tanh x = 12/13, find the values of the other hyperbolic functions at x.  *please use hand writing…

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Q: The rate of growth dP/ dt of a population of bacteria is proportional to the square root of t, where…

A: Given query is to find the population after 6 days.

Q: Find the local maxima and minima for the function ƒ(x) = |x² + 4x − 5|. If there is more than one…

A: We have given function  fx=x2+4x-5 fx=x2+5x-x-5 fx=xx+5-1x+5 fx=x+5x-1 Range of the function is…

Q: Sketch the situation if necessary and use related rates to solve. 1) Two buses are driving along…

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Q: Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate…

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Q: Solve the given differential equation (where the function is subject to the given conditions) by…

A: Given, y"-4y=8e3t, y(0)=4, y'(0)=0

Q: Evaluate the limit, if it exists. 1 - 2x² - x4 5+x - 3x4 1 2 (i) lim x → ∞

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. Sketch the domain of the following functions: a) f(x, y) = b) f(x, y, z)= 2-x-y - eª %2 In(4-x² -…

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Q: 9. Find each partial derivative : (a) 8³% дудх2' (b) ეპიც əxəyəz' for z = ln (sin (x − y)). for w=…

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Q: Find lim h(x), if possible. (a) h(x) = f(x) = -8x² + 3x - 4 f(x) X lim h(x) (b) h(x): f(x) lim h(x)…

A: Concept: A function may get close to two distinct limits. There are two scenarios: one in which the…

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: The differential equation is given by f''x = x-32                                   ...........1 The…

Q: Find the absolute extrema of the function over the region R. (In each case, R contains the…

A: We have to find the absolute extrema.

Q: Give the general solution of the given ODE. Show full solution. y′(2x−3) = 2xy+48x−3y−72

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Q: 41. lim [2ln(x-3) - In(3x² + 5)] X-80

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Q: 3. Sketch the vector-valued function r(t) = (sin(2πt), t, 3 cos(2πt)), indicating direction.

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Q: Consider the differential equation y'' + 6y' +9y = 0.

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Q: Divide using long division. State the quotient q(x) and the remainder r(x) 8x cubed - 5x squared +…

A: Solution- Given Dividend=8X3-5X2+9X+2 Divisor = 8X2+3X+5 remainder =? quotient q(x)=?   by Long…

Q: Let P be the plane that intersects the x-axis at the point (1, 0, 0), the y-axis at the point (0, 2,…

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Q: The graph of the curve given by the parametric equations: x = 2 cosht, y = 3 sinht is O a circle O a…

A: NOTE: Refresh your page if you can't see any equations. .