Given that z= Inx2+y? +tan- then the value of will be ax? ay

Q: With the aid of residues, and a carefully chosen contour, show that d.x x5 +1 5 sin(T/5)

A: We we solve the general form of the integral for n instead of 5 Then we will substitute n=5 in order…

Q: az If z? = y sin(xy), find ду at the point (-1, ",1) a) - 0.5 b) 플+1 c) - 2 d)-플- 1 e) 0 f) 1 g)…

A: We have to find the direction derivative from the given condition and partially derivative  at the…

Q: az Q1:- Find the az and ax 2, if Z = x* sin x y, ay

A: In this question we have to find derivatives of z w.r.t x and y . We will use product rule.

Q: If x = e" tan v, y = e" sec v, then the value of y%3D X +y X- +y is

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Q: az and dy az Ql:- Find the if Z = x* sin x y.

A: As per our company guidelines we are supposed to answer only one question.Kindly repost other…

Q: aw and ar Q2) Find if as w = 2x + 4y - z, r+s X =r tan (s), y= sin (r - s), z=e**s.

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Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) - then the domain of r is О 11, 10] (1, 0) O [1, 10) O…

A: Explanation of the answer is as follows

Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

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Q: Given, u=x-y Which of the following is correct ? Analytic

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Q: Let p and q be integers with q > 0. If y = x, differentiate the equivalent equation y = x°…

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Q: C A wer.. V Cos A = choose your answer.. Tan A = choose your ans

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Q: af and If f(s, t) = t sin st, find - as at

A: Given,          fs,t=tsinst

Q: EX show that J, (x) 2. sin X %3D zm + Sol:- J CX). = (-) M=D0 m+ LIN

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Q: where D C 0 find amatrix 2 Irand d I is identity 3 -1 1

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Q: The values of C, and C2 so that y(x) = C, sin x + C, cos x satisfies the following conditions: y(0)…

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Q: Define h(*) = J¿r)d* . Then, which of the following are true?

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Q: Find (t), given 7(t) = (– 5t* – 1, 4 sin(2t), 4e*). = (?),

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Q: What is the exact value of cos ZPQR? 3. R. 21 16 7 16 3 16 4. 1/4

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Q: DS tan %) c(x) ax

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Q: If 1 Å : V(x2 + y?) [(хуz — Зху)а, + (zу? + 3x? )а, + ху а,] And B = r2 a, + sin 0 aø Find JÃ x B|…

A: The vector is A→=1x2+y2xyz-3xy ax+zy2+3x2 ay+xy az At P1, 2, 4, A→=152 ax+19 ay+2 az We know,…

Q: If f(x, y) = ln (xy) — 5 sin y, then ƒx(1, ´) = T Select one: True O False

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Q: Show the following differontial quahion is hamegenous and Solve it: X*dy +C y-xy) dx

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Q: Given x = a cos 0 + b sin 0, y = a sin 0 – b cos 0. Using Cramer's rule, find a in terms of x and y.

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Q: t/2 Evaluate using Wallis' Formula: sin? x cos5 x dx

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Q: az az and du #6. Use the Chain Rule to determine given that av z = x sin (y? – x) x = 3u – v?, y =…

A: Solution:-

Q: and <0 < r, then sec(0) %3D

A: We use Trigonometry ratios

Q: Let P = {x € R | sin(x) = 0} and Q = {na | n E Z}. What is the relationship between P and Q?

A: Let P = {x ∈ R | sin(x)=0}, and Q = {nπ | n ∈ Z}. What is the relationship between P and Q​

Q: If z = x2 + y? x = e' cos(s) and et sin(s y = ), then

A: ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s Lets find out each derivative z=x2+y2∂z∂x =2xx=etcos(s) ∂x∂s=et…

Q: az If z? = y sin(xy), find ду at the point (-1, .1) d) --1 %3D b) + c) - 2 а) - 0.5 e) 0 f) 1 g)…

A: We will find the partial derivative with respect to y and then evaluate at the given point.

Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

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Q: If r (t) = (cos(t), sin(t), 2) , then ſr (t) dt =

A: r(t)=&lt; cos(t), sin(t) ,2&gt;

Q: az If z? = y sin(xy), find ду at the point (-1, ", 1) a) - 0.5 b) +1 c) - 2 d) -- 1 f) 1 e) 0 g)…

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Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: Determine all values z ∈ C satisfying  e^z = −2i.

A: ANSWER :

Q: A GIVEN: AB I BD, ED I BD. PROVE: XA = XE. C

A: We will use these three concept here  1- perpendicular makes an angle of 90° 2- vertical angle are…

Q: F k d

A: Use conic section we can prove it.

Q: Let r(t) = (sin 3r, cos 3r, /īt), Find T(t) and N(t)

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Q: Find the exact values of s in the given interval that satisfy the given condition. 2. [0, 2n); tan…

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Q: If P = 2 sin(10t + x − π/4)ay and Qs = ejx (ax − az)sin πy, determine the phasor form of P and the…

A: Given- If P = 2sin10t + x - π4ay and Qs = ejxax - azsinπy To find- Determine the phasor form of P…

Q: T/2 Evaluate using Wallis' Formula: sin? x cos5 x dx

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Q: The identity S dyd x f, dxdy is %3D O False True

A: We need to check whether the given Identity is True or False.

Q: given z=x2-y2, x=r cosθ, y=r sinθ, find ∂z/∂θ

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Q: Given APOR -AXYZ, which must be true? Select all that apply. A PQ PR ZX B. mZP X7u OC. QR YZ D. m/R=…

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Q: Given that sin x+y3=ax2y, express y' in terms of x and y.

A: Objective is to find y'.

Q: If So S, (x² + y² ) sin(x)dxdy= f L (2²² + y?) sin(x) dydæ a , then a, b are

A: Solution is below.

Q: d Q3/ By using definition, proof that cot x = – csc² x . dx |

A: Derivative of cotx with respect to x is csc2x.

Q: S(1,9) =2Inc* + y° )• 3y° tan"), then prove that B.(i) If дхду дудх

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Q: If r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

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Q: x sect and y= tant, evaluate at t = - of the follow 4 dy (b) d y dx?

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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.