SUppose that y is continous function over the interval Lo,5] Also suppose we know the following 0 gaJ dx = 2 find the following given 3 g) k bIS (2g u9-3) de c) Let GGO =S t? sin+?)dr find bi 8) %3D

Q: 7. f cos xdx

A: The given integral is Cos4x

Q: Which function has the same graph as y= 4 cos y = 4 sin x+7 ) y = 4 sin 3 y = 4 sin X- y = 4 sin

A:

Q: Evaluate each of the following: (a) /" In(x) dx

A:

Q: 3) Evaluate ex*+¹sin (√x) dx].

A:

Q: dx Evaluate x²/4 x²

A:

Q: b) sec(arcsin x2+4, 以a sin g 孙 OPP Los : als hyp a-t6-cと とい ))Not how sec = x-Vxty %3D exponent…

A:

Q: The S- 3 dx is 5 sin 6x

A:

Q: 4. Evaluate tan (4.3 – j1.1).

A: Given that, evaluate tan (4.3 - j1.1).

Q: Which is the greater rate,15 miles in 12 minutes or 25 miles in 20 minutes?Explain

A: Solution: the objective is to find sum of given series

Q: Can you please help me out with question 7?

A:

Q: Let x² + sin(yz) = xz² + y dz and ду dz Find

A: Given,           x2+sinyz=xz2+y

Q: #6. Eunlwate taldx uhere cosk fa) cosx-SinZx, x)n .

A:

Q: 11. The derivative of cos 3x² is: a. -6x sin 3x² cos 3x² b. - sin 3x² c. -6x cos 3x² d. -6x sin 3x²…

A: Derivative represents the rate of change of a variable with respect to the independent variable. A…

Q: 1) Determine the derivative o a) f(x) = -4e*² b) y = cos(3*) c) g(x) = -2 sin3 (2x) %3D %3D

A: Note: Multiple subparts are given, we are answered with first three parts only, if you need more…

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

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.