lim x2

Q: (a) COMPUTE the dimensions of the rectangular box of maximum volume that can be x² + y? + z? = 4. in...

A: Since you have posted multiple questions, we will solve only first question for you. To get remainin...

Q: Write the equation ln A = 3 in exponential form.

A: We will use the exponential form of the natural logarithm.  

Q: QUICK CHECK 3 Let u(t) = (t,t, t) and v(t) = (1, 1, 1). Compute d (n(t) • v(t)) using Derivative dt ...

A: given vector  Here use product rule : ---------------(1) Now we need to find derivative of u'(t) a...

Q: Use multiplication or division of power series to find the first three nonzero terms in the Maclauri...

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Q: Find the interval of convergence of the series Σ 27n(x-4)3n+2 from n=0 to infinity

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Q: Simplify 35a14b6 / -7a7b3

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Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

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Q: Find a particular solution of y" - 6y' + 9y = e3x

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Q: Look at image

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Q: Find the area of the sector of a circle with radius 13 meters formed by a central angle of 180": squ...

A: To determine: The area of the sector of a circle with radius 13 meters formed by a central angle of ...

Q: Estimating errors. Use the remainder to find a bound on the error in approximating the following qua...

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Q: Find ∫5 cos 5x dx.

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Q: 1) Let h(x, y) = x* – 4xy² – 2x² + 8y². Find and classify all local extrema of the surface using the...

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Q: The number of US cellular phone subscribers (inmillions) is shown in the table. (Midyear estimates a...

A: Since the problem contains multiples sub parts  so here is the solution of only two parts for the re...

Q: A truck with 22-in.-diameter wheels is traveling at 50 mi/h. Find the angular speed of the wheels in...

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Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus b...

A: We need to Integrate fo find F as a function of x.

Q: Evaluate the integral, if it exists.  ∫01 y (y2  + 1)5 dy

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Q: Refer to image

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Q: Find the left-endpoint approximation for the area under the curve f(x) = x2 on the interval [0, 2] u...

A: Given

Q: Sketch a graph that has a vertical asymptote at x=2 and a horizontal asymptote of y=1, and identify ...

A: Given that, the graph has a vertical asymptote at x=2. The vertical asymptote occurs where the denom...

Q: Find the area (in square units) of the region under the graph of the function f on the interval [−2,...

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Q: +y 2. mations

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Q: Find the interest rate needed for an investment of $6,000 to grow to $10,000 in 4 years if interest ...

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Q: Q4. a) Without using the shift formula prove that Laplace of f(t) =e sin wt is (s+a) +w²

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST QUEST...

Q: Evaluate the definite integral using the given values

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Q: Suppose you start at the origin, move along the x-axis a distance of 7 units in the positive directi...

A: To determine: The coordinates of the position when starts at the origin and move along the x-axis a ...

Q: Suppose you are solving equations in the interval [0, 2π). Without actually solving equations, what ...

A: We have given the two function of sin; sin x = 1/2 and sin 2x = 1/2

Q: Refer to image

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Q: Sketch the graph of a smooth function ƒ and label a point P(a, ƒ(a)) on the curve. Draw the line tha...

A: The aim is to find the graph of a smooth function and represent the line which shows the linear appr...

Q: Maximize f(x,y)=x2+y2 subject to the constraint 2x+6y=26 the last question is what is the maximum va...

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Q: Calculating derivatives Find the derivative of the followingfunctions. y = tan x + cot x

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Q: How do I differentiate the function y=e^tan(θ)?

A: y=e^tan(θ) We need to differentiate the function

Q: Shown is the graph of traffic on an Internet serviceprovider’s T1 data line from midnight to 8:00 AM...

A: Given that, The T 1 data line from midnight to 8.00 am is represented by graph. The T 1 data line tr...

Q: ayer in čéntér field is approximately b 370 feet from a television camera that is behind home plate....

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Q: Find the angle between the two planes x − 2y + z = 0 and 2x + 3y − 2z = 0. Then find parametric equa...

A: The equation of two planes are x-2y+z = 0       ...... (1) 2x+3y-2z = 0   ...... (2) Angle between t...

Q: Bioavailability The most efficient way to deliver a drug to its intended target site is to administe...

A: Given: Two functions To find: Bioavailability of the drug Formula Used: Bioavailability of a drug i...

Q: 8x) dr

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Q: Find the singular solution of the partial differential equation: az az z = px + qy +p² + q? where p ...

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Q: Find the slope of the function's graph at the given point. Then find an equation for the line tangen...

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Q: Describe how the name hyperbolic function arose

A: Consider the equation of the semicircle is, Consider the equation of the hyperbola is,

Q: Find the critical numbers of f(x) = x 3/5  (4 -x )

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Q: Use limits to find the derivative function ƒ′ for the followingfunctions f.b. Evaluate ƒ(a)for the g...

A: a) Using the limit definition of f'(x) we get:

Q: Find the values of the trigonometric functions of t from the given information. Find exact values, n...

A: Given that csc(t) = 5 We need to find the all other 5 trigonometric functions.

Q: Aiming a tangent line Given the function ƒ and the point Q,find all points P on the graph of ƒ such ...

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Q: Curvature Find the unit tangent vector T and the curvature k for the following parameterized curve.

A: We have given the function;

Q: f(x) = 6x3 - 9x - x5 a. Use the Leading Coefficient Test to determine the graph’s end behavior.b. Fi...

A: f(x) = 6x3 - 9x - x5 “Since you have posted a question with multiple sub-parts, we will solve the fi...

Q: graph the points z = x + iy that satisfy the givenconditions. | z + 1| = | z - 1 |

A: It is given that With the condition Substitute the value of z in (2)  

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.