sqrt(5-2x^2)<_f(x)<_sqrt(5-x^2) for -1<_x<_1, find limx->0 f(x).

Q: Find the limit of limx->-1 (x3-2x2+5)

A: Since this is a polynomial function,we can calculate the limit by direct substitution. We have The…

Q: 4) evaluate lim x-->2 (2x2 - x - 6) / (x2 - x - 2)

A: Explanation of the solution is given below...

Q: sinx Find the value of the limit lim x →0 2x

A: To find the value of the given limit.

Q: Suppose limx →4 ƒ(x) = 0 and limx →4 g(x) = -3. Find lim x →4 g(x)/ƒ(x) - 1

A: We first distribute the limit

Q: How do I compute  limx→4(x^2−6x+8/x^2−4x)

A:

Q: Find limx-&gt;∞,if for all x&gt;5

A: We apply limx-&gt;∞ on all sides.

Q: Calculate the limit limx→0+(arcsinx)2x.

A:

Q: If lim f(x)=-2 x-->0+, lim f(x)=3 x-->0-, and f(0)=-2, what can you say about lim f(x) x-->0?

A:

Q: Evaluate limx--&gt;2 (sin(x-2))/(x^2+4x-12) Without L'Hospital's rule.

A: limx--&gt;2 (sin(x-2))/(x^2+4x-12)Numerator = sin(x-2)Denominator = x2 + 4x - 12 = x2 +6x - 2x - 12…

Q: show that : Limx→0    1/ (x – 1) + 1/( x + 1)  ) /x = −2

A: apply the concept of limit to prove the given problem.

Q: Use a tble of functional values to evaluate: lim 12 z-2

A:

Q: Use a table of values to estimate the value of thelimit. If you have a graphing device, use it to…

A:

Q: The value of lim (xe- x) will be ...

A: It is given that limx→∞xe-1-x.

Q: Evaluate the limit: 2x +10 lim x-5 x +2x -15 lim as x -> -5 of |2x + 10|| divided by x ^ 2 + 2x – 15…

A: Evaluate the limit

Q: What are limx→+-∞ k (k a constant) and limx→+-∞ (1/x)? How doyou extend these results to other…

A: limx→af(x)=L means f(x) becomes arbitrarily close to L as long as x is sufficiently close to a.  We…

Q: If limx→0+ ƒ(x) = A and limx→0- ƒ(x) = B,find limx→0+ ƒ(x3 - x)

A: Given: limx→0+fx=A,limx→0-fx=B we have to find limx→0+fx3-x we know that if x∈0,1 then x3&lt;x

Q: x-sin 2x Find lim 2х

A:

Q: 1. lim→- Зx? (2х - 1) 1 + 4x + 3 9. limx--3 x2- 3 2.

A:

Q: lim (In 2x + 5) + 4 X-1

A: From the given problem:   limx→-1ln2x+5+4   As we know that:   limx→afx±gx=limx→afx±limx→agx

Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

Q: 2-V2(3x+1) 2x limx-1 X-1

A: we have to calculate;  limx→12x2-2(3x+1)+2x-1

Q: Suppose that ƒ is an odd function of x. Does knowing that limx →0+ ƒ(x) = 3 tell you anything about…

A: Given that f(x) is an odd function.  So, f(-x)= -f(x) Given that lim x →0+ ƒ(x) = 3

Q: Find lim Sin (X+2) X->2 x4x-2

A: Explained below

Q: : limx->0(1/x3)

A: We have to simplify the given expression. The given expression is limx→01x3∫0xt2t4+1dt

Q: Evaluate limx--&gt;0 (sin^2 2x)/(2x) Without using L'Hospital's rule.

A: The given funtion is (sin^2(2x))/2x for the limit x tends to 0.

Q: Find lim tanx-x x2 sinx X

A:

Q: Evaluate lim-[(sinx-x)/x³] by u

A:

Q: If lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say…

A:

Q: If limx→0+ ƒ(x) = A and limx→0- ƒ(x) = B,find limx→0+ ƒ(x2 - x4)

A: Given: limx→0+fx=A, limx→0-fx=B we know that when x=0+, f0+2&gt;f0+4 so, given limit will be…

Q: Suppose limx →4 ƒ(x) = 0 and limx →4 g(x) = -3. Find lim x →4 xƒ(x)

A: It is given that limx→4fx=0 and limx→4gx=-3.

Q: Find limx approaching infinity (x+2/x-1)^x

A:

Q: 1) lim-sinxr x-0

A: given equation is     limx--&gt;0  (x-sinx) / x³ ** L hospital rule =&gt;    limx--&gt;0  f(x) /…

Q: Create a table of value (use 8 values - 4 on the left and 4 on the right) and a calculator to the…

A: Given problem:- Evaluate limx→610-x-4x+6by using 8 values table 4 left and 4 right

Q: Find the limit of the equation.

A: Given limit

Q: Find  lim x+8/x-1 as x approaches -2 approaches

A:

Q: In x 35. lim

A:

Q: lim (-Y" 2. スーラ ル

A: Sure.

Q: 2x-√5+4x lim x→6 x-3

A: The given limit is limx→62x-5+4xx-3

Q: 4- lim Vsin x

A:

Q: lim (x2 + 2)sechx

A:

Q: - lim SinTX メー→ メ ー」

A: We need to evaluate limx→ 1sinπxx-1.

Q: 4 ) lim- (x-.tanx 17

A: Use simple result of limit

Q: Determine limx→−2 6/x-2, if it exists

A: limx→−2 6/x-2 yes limit exist and we can direct apply the limit so put -2 in given function…

Q: 2tanx-sin2x 6. lim X0 x3

A:

Q: If sqrt(5 - 2x2) &lt;=ƒ(x)&lt;= sqrt(5 - x20 for -1&lt;= x&lt;=1, find lim x--&gt;0 ƒ(x)

A:

Q: Suppose I tell you that limx→6 f(x) = π. What can you conclude about limx→6+ f(x) and limx→6− f(x)?…

A:

Q: Find the limits limx→∞csc-1 x

A: Given:limx→∞ csc-1x

Q: B) Without using L'Hopital's rule, find: lim 3-Vx2+9 x2

A:

Q: Estimate lim 16 4 is approaching to using a table of functional values.

A: We will use the L. Hopital's rule to find the limit of the given function. to find limx→ 4(16x-4x-4)

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.