If fiß->(0,4) and I 9s an interval on which fhas both values, then t has Oi discontinutty 9n I,

Q: Q2 Which of s1852 forms abaris Jus tify and find the (corolinates g V=() relative to that bazis:

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Q: Find the interval on which the curve 1 dt 3+t+3t2 y = 1 is concave upward. Note: When using interval…

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Q: The graph of y =| f(t) dt , where fis a piecewis shown here. yA 2- 2 4 -1+ -2+ Over which intervals…

A: In this question we will use basic of calculus i.e concept of function. We will simply observe the…

Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Sol:- By applying extrme value theorem frection                      has to be continuous on x E…

Q: 1srs0, then (i) Test whether the Rolle's theorem holds for the function f(x)=D< In 0<xsl the…

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Q: Let =)4.i8 0<x<1 f: [0,3]-R defined by fo %3D 3,if X=1 5, if <X< 3 show that feBra and thab fa.dx =…

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Q: Which of the following functions of is guaranteed by the Extreme Value Theorem to have an absolute…

A: To identify the function guaranteed by the extreme value theorem to have an absolute maximum on the…

Q: Find y" by imprcit differen fia fên. Simpliey unenoven Po Ssiole

A: Given:- x2 + 9y2 =9  To find:- y'' of given equation

Q: An aiplane's velocity is recorded at 5-min intervals duning a 1-hour period with tme following…

A: We have to find distance travelled by airplane using Simpson's Rule.

Q: 1 Find the interval on which the curve F(x): -Sa di is concave downward. 6+ 8t

A: Solve the following

Q: For what value of the constant c is the function f continuous on the interval (-o, 0o). - Scr+ 3z, I…

A: Explanation of the answer is as follows

Q: Da² + 42x + 5: (i) local minima and max (i) intervals where fis co

A: Dtermine (i) local minima and maxima of f,(ii) intervals where f is concave up and concave…

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: (b) Evaluate R dx using Simpson's one third rule with 6 intervals

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Q: 2. STO Find the length of the graph of y = 2+ In(sin z) om the interval [7/4, 7 /2].

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Q: find the nUmbers b such that the auerage due of f(x)2+6x-3x on the interval E LO,b) is equel to 3

A: Average value of function is given by taking the integral of the function over the interval and…

Q: Vx4 + 39x + 13 – 4 = 0

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Q: 2. Find the intervals where f(x) = x + cosx is concave up or concave down on [0, 2Tt]. Find the x…

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Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Option (C) is correct. Because the given function is continuous in the interval [0 4].

Q: Given f(x) = In(x² + 3x + 9), over the interval [ – 5, - 1], answer the following: %3D a) The point…

A: Given,           fx=lnx2+3x+9

Q: If g(t)=t^2tan(t), then can the Intermediate Value Theorem be used on the interval [0, pi/4] to show…

A: If a continuous function in a domain has two domain end points and one point is above the required…

Q: 2. k) Show that fe2) = function is analytic %3D t'+s for Rez 70.

A: Calculate the limit: lim∆z→0fz+∆z-fz∆z=lim∆z→0∫0∞e-tz+∆zt2+1dt-∫0∞e-tzt2+1dt∆z…

Q: (+²+ 2) y² - 4 ty=4t, y(0) = 3

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Q: If we try to apply Rolle's Thorem to the function f(x) = 2x² – 20x – 5 on the interval [0, 14],…

A: Here, the given function is: f(x)=2x2-20x-5 and the interval given is [0,14].

Q: Find the sign of the following. sec (-0), given that e is in the interval (180°, 270°). O positive O…

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Q: Which of the functions satisfy the hypotheses of theMean Value Theorem on the given interval, and…

A: Given The function is f(x)=x2-x-2≤x≤-12x2-3x-3-1&lt;x≤0   Mean value theorem :- let f be the…

Q: f(x) = x³ – c to answer rval(s) on which f(x) is ir

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Q: Given f(x) cos r, determine all values of x in [0, 27) where f(x) has a horizontal tangent.

A: We have to find the value of x

Q: A vehicle accelerates from rest, and the time it takes to reach the speed v, is given by the…

A: Here we have to calculate the time taken by the vehicle to reach the speed of 50m/s…

Q: If a ton K holds K000 Aallons of watev, the dan k after t minutes 9s giren by V= d000 (! which of…

A: The capacity of the water tank = 8000 gallons   The volume of water which remain in tank after t…

Q: The height of a ball t seconds after it is thrown upward from a height of 7 feet and with an initial…

A: solution :- The height of a ball t seconds after it isthrown upward from a height of 7 feet andwith…

Q: Q2/ Use the Simpson's and trapezoidal rules with n-8 to estimate f(x2 +2)dx and determine which rule…

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Q: Find the smallest value ofn such that the remainder estimate |R.s M -(x - a)" + , where M is the…

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Q: 2. The gragh of g is given as following. (a)At what numbers is g discontinuous? Why? (b) At what…

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Q: y' =+y(y+2), y(0) = - 1

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Q: Find the root within a given interval in the following function by secant method up to 5s (a) In x =…

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Q: Show all steps to verify that fry = fyx given f(x, y) = cos(2x) – x²e5y + 3y²

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Q: Compute the length of the curve r(t) = (21, In(?), r²) over the interval 1 < t < 7. (Use symbolic…

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Q: el+x By using the definition In(1+x) = 1 -dt, show that for a certain range of values of r,…

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Q: 3. Given that f(r) = dt. Determine the interval(s) on which f is increasing. %3D 3+t

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Q: Q2. Let f(x) - In(cos x) (i) Find the are length (ds) of the function

A: Given,                f(x) = ln(cos x) ⇒y=ln(cos x) ⇒ dydx=-sin(x)cos(x). And we have to find arc…

Q: ® find the absalute Max. oud absolute min for the Rollawiny functions intervals o Cn the giくen if…

A: According to our guidelines we can only answer 3 subparts at a time, rest you can repost later

Q: The abetute uinian value of f(r)--3r 12 on the closed interval -2, 4ceurs at aM (A) 1 (B) -1 (C) 0…

A: Given:   f(x)=x3-3x2+12   in interval [-2,4]To find absolute minimum applying first derivative test…

Q: is st L- and at most U - 280 Select an answerY In the interval. Select an answer the hypothesis.

A: *Answer:

Q: (2 Assume that finis define and peioclic with s how that if f for au x peiad T, tubegrable n for…

A: assume that fx is define for all x and periodic with period T to show - if fx is integrable in 0≤x≤T…

Q: dy +. (x>0) tind the Soiution of the difperential equation, expressing 4explicitly as general 4…

A: First we comparing the given differential equation with dy/dx+Py=Q .and then find I.F. and then…

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.