If f is differentiable at a , then f is continuous at a . True O False

Q: If f is continuous on A) True B False on [a,b], then Sº [ f(x a xf(x) dx = x f(x) dx

A: It will solve by part method integration  ∫u v dx = u∫v dx −∫u' (∫v dx) dx u is the function u(x) v…

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist.…

A: The given statement is

Q: Answer true or false. If f is not piecewise continuous on  [0, ∞>),  then  ℒ{f(t)}  will not exist.

A: Given problem:- If f is not piecewise continuous on [0, ∞),then ℒ{f(t)} will not exist.  True…

Q: If f is continuous at a, then f is differentiable at a. O True O False

A: Answer: False.

Q: Answer true or false. If f is not plecewise continuous on [0, 00>), then {f(t)} will not exist. O…

A: Note that, L{f(t)}=F(s)=∫0∞e-stf(t) dt...(1)

Q: If f is continuous on [a, b], then there is cE[a, b] such that f(c) = av(f). Select one: True False

A:

Q: If f(x) is continuous everywhere, then If(x)| is continuous everywhere. TRUE O FALSE

A: If f(x) is continuous everywhere, then |f(x)| is continuous everywhere.True of false.

Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then L{f(t)} will not exist. True…

A: Given: Lets consider the given, that Lft will not exist if f is not piecewise continuous on [0,…

Q: 6. Provide a counter example and explain that the following statement is false. "If f is continuous…

A: We want to find a counter example of given statement.

Q: If f is continuous and even on [-a, a], then f(x)dx = [ ` f(-x)dx Select one: O True False

A: Take Left-hand side∫-aafxdx, Use the property for fx continuous on a,b, ∫abfxdx=∫abfa+b-xdx

Q: Let f be continuous on [a, b] and suppose that f(x) 2 0 for all x e [a,b]. Prove that if L(f)=0,…

A: Given: Let f be continuous on [a,b] and suppose that f(x) is greater than or equal to zero for all x…

Q: Answer true or false. If f is not piecewise continuous on [0, ∞o>), then L{f(t)} will not exist. O…

A:

Q: If f is continuous everywhere, then af(bx) dæ < af(bx) dx, where a and b are real numbers. -3 O True…

A:

Q: Suppose that f is continuous at 0, and that f satisfies f(x + y) = f(x)+ f(y) for all real numbers…

A:

Q: f is continuous at a if and only if |f| is continuous at a.

A: False

Q: If f(x) is differentiable at x = a then f(x) is also continuous at x = a. A True B False

A:

Q: Let f : X 'n Y be a continuous function. If X is disconnected then so is f(X). True False

A: As image of a connected set is connected in of every continuous function.

Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then L{f(t)} will not exist. O…

A:

Q: if f(x) is continuous on[a,b] then -S f{x)dx) = f(x) dx Select one: O True O False

A:

Q: Assume f(x) is continuous on [a, b]. Prove that if f(x) > 0 for all x € [a, b], then S. f(x) dx > 0.…

A: Extreme Value theorem states that if a real-valued function f is continuous on the closed inteval…

Q: If a function f is not defined at x = a then it is not continuous at x = a. Select one: O True O…

A: As we know that a function f(x) is said to be continuous at x=a when the right-hand limit and…

Q: Suppose f and g are continuous functions on the interval [a, b], then SEAFX) – g(x)) dx = [." f(x)dx…

A:

Q: Ler f : R → R be continuous. If f(c) > 0, prove there exists a neighborhood N of c such that f(N) >…

A:

Q: O No, because f is not continuous on the closed interval [a, b].

A: Given that: The function f ( x) = x2 - 81x - 4     ,  [ -9, 9  ]  .

Q: 4. Let f:A→R and g:B→R where f(A)cB. Explain to prove that if f is continuous at CE A and g is…

A:

Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then {f(t)} will not exist. O…

A:

Q: Determine whether the statement is true or false. If f is continuous on [0, o0) and f(x) dx is…

A:

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist. O…

A: For the solution of the problem follow the next step.

Q: Let f(x) = 0 if x∈Q if x and f(x) = 1 if x ∈R\Q. Prove that y=f(x) is not continuous at any point…

A:

Q: 1 - is continuous at a. f If f(x) 0 for all x in the interval I, and f is continuous at a in I then…

A: 1/f is rational function this is discontinous where either f is discontinous or f is zero  But f is…

Q: If f(x) is differentiable at c, then there exists d > 0 such that f(x) is continuous in (c – 8, c+…

A: We have to define it is true or not

Q: Suppose f is continuous ont he closed interval [a, b). If F(x) is an antiderivative of f(x), for…

A:

Q: If f is continuous on [a, b] and cE[a, b], then f(x)dx does not exist. Select one: True False

A: Topic:- definite integration of continuous function

Q: If f and g are continuous at c, then fg is continuous at c. Select one: O True O False

A: If two functions f(x) and g(x) are continuous at x =a then f(x).g(x),  f(x)/g(x),   f(x)+g(x) and…

Q: If f is continuous and even on [-a, a], then f(x S'f)dx = [ °ft-x)dx Select one: O True False

A: f is continuous and even on [-a,a] , then ∫-aaf(x)dx=∫-aaf(-x)dx

Q: If f is continuous on [a,b], then [a,b], then A) True B) False [ f(x)dx = πf f(x) dx

A:

Q: If f is continuous on [a,b], then f(x)dx= π + A) True B) False f(x) dx

A: Given that f is continuous on a,b. ∫abπ fx dx = π ∫abfx dx Say that the statement is true or false.…

Q: Determine whether the statement is true or false. If f(x) is continuous at x = c, then so is f(x).…

A: Solution is given as below:

Q: Answer true or false. If f is not piecewise continuous on [0, co>), then L{f(t)} will not exist.…

A: Solution

Q: If f is continuous on [a, b] and f'(x) 0 O f(b) f(b)

A:

Q: Suppose that f is continuous on [a.b] that f(x) 20 for all xE[a,b] and that f =0 1. Prove that f(x)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

A:

Q: 1. Given that f is continuous on a, b|, compare f(b)(b – a) | f(x) dx, and if f is constant on a,…

A:

Q: If f(x) is continuous everywhere, then square root of f(x) is continuous everywhere. * O TRUE O…

A: We have to find out if f(x) is continous everywhere then square root of f(x) is continuous…

Q: Suppose f is continuous and F'(x) = f(x). J s(x)dx =3, f(x)dx = 4, [f(x)dx= 5, and F(1) =6, evaluate…

A: Here this is simple application of integration and differentiation please watch carefully.

Q: True o false ? If fand g g are Continuous on faib I, then

A: Please see the answer below.

Q: If f:R → R is continuous at both 2 and 4, then f must be continuous at some c E (2,4). Select one:…

A: Consider the function f:R→R, that is continuous at both the points 2 and 4. Let there be a point c…

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.