In calculus integrals , limits and derivatives are some of the subjects . What are the reasons that make these topics more appealing ? explain in detail

Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: Express the limit as a definite integral on the given interval. COS X¡ lim Дх, [Зл, 5л] Xi i = 1 dx…

A: This question is related to definite integration, we will solve it using given information.

Q: Is the functions continuous at the point being approached? lim tS0 sin(pi/2 cos (tan t))

A: Here given function as ft=sinπ2costan t⇒f0=sinπ2cos tan 0=sinπ2cos 0=1

Q: Express (3*) dx as the limit of a sum. 1

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Q: 2. Find the following improper integral. 00 - 0.1x dx 1

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Q: Find the points of discontinuity of the function f(x)=arctan1x if they exist.

A: The given function is not defined at x = 0. Now the left hand limit at x = 0 is, And the right hand…

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Q: Choose True if the statement is correct, otherwise False. If a function is odd, its definite…

A: The given statement is  '' If a function is odd, its definite integral from a to b will always…

Q: If the limit of f(x) is 1 as x approaches 1 and the limit of g(x) is infinity as x approaches 1,…

A: we have to find the limit of the following

Q: What conditions must be satisfied by a function if it is to be continuous at an interior point of…

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Q: Find the equation of the tangent line of f(x) = sqrt(x+1) at x = 0 using the definition of limits.

A: To find: The equation of tangent of line. Given: The function is f(x)=x+1. Concept used: Slope…

Q: Find the linerization  of f(x)=x^3  near x=1 . use that linerization to approximate (1.1)^3

A: Linearization of f(x) near x=a is given by f(x)=f(a)+f'(a)[x-a] Where f'(x) is first derivative of…

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Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: At what points are the functions continuous? x + 3 f(x) 2 - et

A: The given function is fx=x+32-ex

Q: What are the requirements for continuity function?

A: For a function fx to be continuous at x=c if it satisfy the following conditions: a) Function should…

Q: If f(x)=tanh^-1 square root x to the fourth power then f'(x)=

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Q: What is the Extreme Value Theorem for continuous functions?

A: Extreme Value Theorem According to this theorem, if a function y=fx is continuous in a given…

Q: Explain why the function ƒ(x) = sin (1/x) has no continuous extension to x = 0

A: Then we can extend the definition of the function at that point to make it continuous there.

Q: Explain why the two forms of Green’s Theorem are analogs of theFundamental Theorem of Calculus.

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Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: How is integral calculus related to differential calculus?

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Q: Could the limit as xà1 of f(x)=(x+sinx)/(1+x+cosx) be found simply by substituting 1 into the…

A: Given function f(x)=(x+ sin (x))/(1+x+ cos (x)) Now we will evaluate limit of f(X) as X tends to 1…

Q: Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but…

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Q: Please show all work:  Is f(x)= x2+3 continuous at x=1? Why or why not? (A rigorous mathematical…

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Q: you were asked to find critical points. What makes something a critical point within the study of…

A: The points at which the first derivative of the given function vanishes are called the critical…

Q: How can we use the general definition to prove the theorems?

A: Query- How can we use the general definition to prove the theorems. Answer- A theorem is a statement…

Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

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Q: Express the limit as a definite integral on the given interval. x₁* lim Σ -Ax, [1,4] n10 (x)² + 7 i…

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Q: Find the limit of the trigonometric function.

A: The given expression is limx→0cosx-sinx-12x

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

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Q: Explain in your own words what the Fundamental Theorem of Calculus says. Be sure to address both…

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Q: Use the limit definition to find the slope of the tangent line to the curve f(x) = square root of…

A: The given curve is  f(x)= y = √(x + 2).. (1)

Q: It is known that f(x) = sin(x). Estimate f'(0.6) and f''(0.6) using the 3-point central formula with…

A: Given fx=sinx and h=1 and h=0.5

Q: 5 f(x) %D sin x

A: Given  f(x) = 5sin x We have to check the continuity of the function on the interval [0, 2π].

Q: Can someone explain tangent for more as well as limits. *all of this within calculus *

A: Please see the below picture for detailed solution.

Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: based on what we know a function to be today, what did Euler mean by an analytic expresstion?

A: According to Euler, An analytic expression is an expression formed from operations such as addition,…

Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: Based on the Fundamental Theorem of Calculus, show in two statements what may be vrong with the…

A: SOLUTION: 1. We have to consider limit of integration (-1,0) to (0,3) .    when , we are going to…

Q: Use the Definition of a Definite Integral or Theorem 4 from Section 5.2 to find the exact value of…

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Q: Determine whether the function is continuous at the given point. Show your solution. h(x)=csc(x) at…

A: Given: h(x)=csc(x) x=π To determine the continuity of the function determine the limits

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: Is f continuous at x = 1?

A: The condition of continues function is, limx→a+fa=limx→a-fa=fa   For limit of function from the…

Q: Find the exact value of the function: 0 6 arccos (-/-)

A: See this solution in below

Q: find f'Cx) if f(x) = In xa

A: We have to solve the derivative

Q: Is it possible to get the exact value of the definite integral of a function using Trapezoidal Rule…

A: No,  Trapezoidal Rule and Simpson's 1/3 Rule not give the exact value of the definite integral of a…

Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

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