lim x o \x +c (x – ' 4

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

Q: 10. Find the value of the limit or state that it does not exist (DNE). a) lim f(x)= =(x)s u X -3

A: Given

Q: Q2. Let f:R- R be a function such that f(x) = x sin| f is defined at x, , where the value of d…

A: Topic- Limits

Q: a) limn-o fn(x) for each r E [0, 1], and b) lim,- So fn(x) dx.

A:

Q: Find the value of c that makes the function continuous at x = 0. SNIPP

A: Hence it is given that the given function is continuous, so we can write:…

Q: Find a formula for LN for f on [0, 2] and compute

A: To Find: ∫02fxdx by taking the limit. Concept: For any function fx that is continuous on the…

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

A: f(x)=x3, a=-2

Q: Consider the function f(x) = vx for xE R and 0 <x < 32. Prove that lim,-s f(x) = 4. %3D

A: Given: f(x)=x for x∈ℝ and 0&lt;x&lt;32 we have to prove that limx→16f(x)=4

Q: Find lim e" dt O 1/e 1

A: This is a special integral function, apply linearity and then solve.

Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: If f is a piecewise continuous and T-periodic, then show that for a e R T ra+T f (x) dx = - (2) f…

A: i used the change of variable formula to obtain solution

Q: (g) Find the value of a and b such that the following limit exists. if x 2. a cos x + 1 sin(5r) x2…

A:

Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 77/2 L(x) =

A:

Q: Find lim e x2 dt X 00 0. ej

A:

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

Q: Find the limit. ey?, P-(5, 0, -5) lim -1 sin O 1 TT оо

A:

Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: S cos (z +1) z<-1 -1<z Let F (x) : e -1 Then lim F (1) =

A:

Q: Choose the correct answer for the following limit Q1_V1_M S sin t3 dt lim x-0 1 2 x4 (A) 3. (B) -1 3…

A:

Q: 3. Consider the following formula f (x) = lim n-0 gn +1 Let D = {x € R: f(x) E R}. Calculate f(x)…

A:

Q: b. b-a Use the equation fte)dx = lim ** ) to evaluate the following definite integral. n-0k=1 2 |(2x…

A:

Q: Let fn(x) n²x²(1 – x) on [0, 1]. Let e > 0. Does lim,0 m ({x € [0, 1]|fn(x) > e}) exist?

A: Given that fn(x)=n2x2(1-x) on the interval 0,1 The objective is to show whether…

Q: e* – 4 , x< 3 - Let f(x) =- cos(x) %3D x2 3 lim f(x) = x 3 O DNE e3 – 4 - O 3 O cos (3)

A: Here we have to find the limit value.

Q: find lim f (x), if it exists. 1– cos z 59. ƒ (æ) = Answer + sin z 60. ƒ (x) = e" – 1 61. ƒ (z) = %3D…

A:

Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

A:

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

A:

Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

Q: Find the absolute extremum point(s) of f(x) = e1−cos x  on [−π/2, π), if any.

A: The given function is                                            f(x)=e1-cos x And we have to find…

Q: [VALUATE THE LIMIT OF THE GIVEN FUNCTIONS: 3 x→1 TT-X² 2

A:

Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

A: We will use Chebychev's inequality to find the required limit of probability.

Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

A:

Q: Given the function f(x) = x² – 2x, what is equation of the tangent line to the graph of f at x = -1?…

A: 1. f(x)=x2-2x at x=-12. f(x) and g(x) are differentiable functions, f'(x)=3x and g'(x)=2x23.…

Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: cos x In(x – a) | 40. lim In(e* – e) X→a+ -

A: Use L hospital's rule when of the form type of inderminate 00.

Q: 3. Convert the limit below into a definite integral and then evaluate it using FTC. 3\²3 1+ n)+2(1+…

A:

Q: Which of the following correctly expresses the limit lim as a definite integral? n5 i=1 1 A. x³ dx…

A: Given query is to find correct integral form

Q: a In(1-x) X lim a-1 So dx

A: We can solve this using series then integral

Q: Find the values of α and β such that the function f(x) =αcosx + 2 if x < 0  and f(x) = βe3x + αx2…

A:

Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

A:

Q: Which of the following correctly expresses the limit lim as a definite n00 n5 integral? 1 A. 1 В. dx…

A: Solution is given as below:

Q: The limit lim e 1+i i=1 n00 can be expressed as a definite integral on the interval [1, 5] of the…

A:

Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A:

Q: Please show step-by-step solution

A:

Q: 1. Find the value/s of b such that the function ƒ is continuous everywhere. f(x) = {6x – sin bx 0 <x

A:

Q: Find lim e dt 0. 1 1/e

A: We find out limit of given function. See 2nd step.

Q: Prove that lim n 00 a" f (x) dx = 0, for any f E R[0, 1].

A:

Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.

Q: Given a function f(x) continuous xeR such that lim f(x)+log(1-1)-log(f(x)) = 0, then f(0) is <

A:

Q: d Prove, through the limit process, that (cos x) = - sin x. dx

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.