write a in the form a = aTT + aNN at the givenvalue of t without finding T and N. r(t) = (et cos t)i + (et sin t)j + √2et k, t = 0

Q: Let csct = V5,t e QII Find sin(2t) 4 O 2 V5 V5 25

A:

Q: ㅠ 6. Let t = Give an exact value for each: 4 (a) sin(-t) (b) sin 2 3 (c) sin(t) 5 (d) sin(2t) (e)…

A: Trigonometric

Q: Determine the fifth roots of z = (4-j5)cos(1+j3). Express your answer in rectangular form

A:

Q: Find the four values of t between -2π and 2π at whichsin t = cos t

A: Our Aim is to find the four values of t between -2π and 2π at which sin (t)= cos (t)

Q: What is csc a if sec a = -4/3 and tan a< 0? А. В. С. D. 4V7 V7 4V7 V7 - 7. 4. 7 4

A: We need to find cscα if secα=-4/3 and tanα&lt;0? A. -477 B. 74 C. 477 D. -74

Q: sinh(3z+1) z2 - 5z+6 Evaluate dz, where C : |z– 2i|= 1, counterclockwise.

A: We have to evaluate ∮Csinh3z+1z2−5z+6dz, where C:z−2i=1, counterclockwise. Cauchy Goursat theorem:-…

Q: Find L(t3 + 5 sin7t).

A: We know that L(tn)=n!sn+1HenceL(t3)=3!s4=6s4 Also L(sin(at))=aa2+s2L(sin(7t))=7s2+49

Q: Use a sketch to find the exact value of the following expression. in-¹(-1)] tan sin Which of the…

A: According to question,Given expression,tansin-1-1517

Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. r(t) = (2 e¹ sin t)i…

A: INTRODUCTION: The formula of the Tangential component of the vector r(t) is given by, aT=v·av The…

Q: Consider the following function. x³ √√²-2² 36 dx (a) Determine an appropriate trigonometric…

A:

Q: Ql:- Calculate the expression sec3.42x-5 +In4 cos30)2-4x 2 where x = 2, y = 5.…

A: Topic-Function

Q: Q3. Evaluate ". -2n sin²0 de 5+4cos0

A: To Determine :-  ∫02π sin2 θ5 + 4 cos θ dθ

Q: C: Proof that ( a) L (cos²t - sin²t) S s² + 36

A:

Q: A bee flies along a path given by r(t) = . Knowing that the bee started on this path at t = 0…

A: rt=sin2ti^+cos2tj^+5t+1k^ Differentiating w.r.t. 'x' to both sides, we get-…

Q: 12. Evaluate: 212-3V+1 (a) (d) / sec (2) / (b) / sec (20) de dr 1 (e) rVI-1 dr dr 16+9r2 (c) sin t…

A: The given integrals are; (a) ∫2x2-3x+1x2dx (b) ∫01x16+9x2dx (c) ∫0π/6sintcos2tdt

Q: tan (t) dt. cos (t)

A:

Q: = (4 – j3)cos(1+j1.5) %3D

A:

Q: tan (t) dt. Evaluate cos® (t)

A:

Q: r2T de Compute 0. 1+ sin 0

A: Given,            ∫02πdθ1+12sinθ

Q: LX X y = Cre²x cos 3x + Cze ²xsin 3x

A:

Q: Use the cosine law to show that ū · ở = ||ū||||J|| cos(0). You must use the cosine law in this…

A: To prove that               u→·v→=u→v→cosθ

Q: An architect designs two houses that are shaped and positioned like a part of the branches of the…

A: Given Equation:- 2025y2-225x2=455,625

Q: A non-right triangle has the following three sides: b = 40.1, c = possible. 45.5, and a = 66.8. Find…

A:

Q: Find all the four square roots of cos(0) +e¡ɛ2 sin(0). Hint: e¡e2e3

A:

Q: TC Compute : exp (sin (e).

A:

Q: k ven Wk-r [cos (+2)+i sin(+2)]; k=0,1,2,3,...n-1 k) Find the cube roots of (1+i). Express Z= e in…

A: The main objective is to find the cube root of 1+i. It is given that Wk=r1ncosθ+2πkn+isinθ+2πkn;…

Q: Solve the problem. For what values of t is r(t) = cos t i + sin t j + sqrt( 9- t2) k continuous?

A: A vector-valued function r(t) is continuous at t=a if and only if: 1. r(a) is defined. 2. limt→ar(a)…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.