(i) (a) Sketch the curves y = 3 and y=e(*+2) on the same diagram. x+5 (b) Given that the two curves intersect at the point (-2, 1) , find the area of the region bounded by the two curves and the y-axis.

Q: 1 dx

A:

Q: dx. Evaluate - 1)²(x² + 2) x+3

A:

Q: can this be done by a human?

A: F(s)=(-4s-2) /(s2-2s+26)

Q: can u show me the work for question a

A: (a) when y = 0,           dy/dx = 0

Q: (c) Give an orthonormal basis for Span {x₁, X2, X3}.

A:

Q: I neeed help with answering quesition 8 part a and b

A: Box plot : It is the graphical representation of 5 number summary for data. Minimum Maximum First…

Q: (b) Give an orthogonal basis for Span {X₁, X₂, X3}.

A:

Q: For the above question, why are they negative?

A: Using All-sin-tan-cos rule we know that: So in third quadrant, only tan and cot are positive. sin,…

Q: 1 -1 A = -1 2 -1 0 -1 1

A: Answer is in next step

Q: Who has an answer for these??

A: Question 1 : If  p and q are true and r is false. That is,  p =T , q = T and r = F Then ( q ∧ r ) ∨…

Q: -5 dt 1+4t? 5.

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

Q: Explain what primary concept does the proof of the Root test use?

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Q: -2 3 -5 2 3 3 2 3 1 1 -4

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.