cot t Differentiate f(t) = et

Q: tan Evaluatee 8 sec dv. tan 8 sec e (Use C as an arbitrary constant.)

A: The given integral is

Q: Find the directional derivative of f at the point P in the indicated direction f(x,y) = arctan y/x;…

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Show that the function e (cos y +i sin y) is holomorphic (anal ytic) and findits derivative.

A: u(x,y)=e^x*cos(y) and v(x,y)=e^x*sin(y) We prove Cauchy Riemann satisfy everywhere

Q: Example: show that u(t)=sin t i + cos t j+ 5k has constant length and is orthogonal to its…

A:

Q: e Transform of f(t) = sin²t By Rule.

A:

Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 7 tan-1 Р(-8, 8); а —…

A:

Q: = * sin (t – 1) dt Find the derivative of the function g( x O sin (3x – 1) sin (2) 3 sin (3x – 1)

A: We will use Newton leibniz formula to solve this question.

Q: Verify the identity.

A: The given expression is sint+costsect+cosect=sintsect Apply the trigonometric identity to simplify…

Q: sin x F(x) = f* Vi dt

A:

Q: sin t - dt = 1 t

A: If f(x) =∫0xsinttdt  =∫0x1t.sint dt Using integration by parts ∫f(t)g(t)dt…

Q: tan¬'(t)+2t² t > 0 t f(t) = t = 0 a ,btan-'(t) t < 0 Find any real number for both a, and b, that…

A: Consider the given function, ft=tan-1t+2t2t   t&gt;0a                     t=0ebtan-1t…

Q: Find F′(x).

A: Given- Fx=∫0sinxtdt To Find- The value of F'x. Identity Used- Using the Labintz rule, we can write…

Q: sin(t)-cos(t)=cot(t)

A: Given problem is sin(t)-cos(t)=cot(t)

Q: sin(T x/ L) E. tan( x) . x2

A: Periodic, non periodic functions

Q: scost 2.) Find the derivative: 1 (t) = (sin" (t²), e² ² lnt>

A:

Q: 3. g(x, y) = cos-1 xy, (1,0), v = î + 5ĵ

A:

Q: Find the directional derivative of f at P in the direction of a. f(г, у, 2) — гу + 2?; P(5, —4, 3);…

A:

Q: sec7(t) tan(t) dt Evaluate indefinite anti-differen

A: We have to find the integral

Q: by using mean value theorem prove |sin(x) – sin(y)I < ]x – y|

A: To prove sinx-siny≤x-y Let f(t)=sint ∀t∈(x,y) Then we have the mean value theorem f'(c)=f(x)-f(y)x-y…

Q: PQ. Use Theorem 13.9 to find the directional derivative of the function at P in the direction f(x,…

A:

Q: sin(t) : 1 sec(t) < 0 %3D

A: The given function is sint=-16 and sect&lt;0. Since, the values of sint, sect are negative, thus the…

Q: Find the Of the : horizontal shift of Sinusodal function -2sin(4t -l) +5 %3D

A:

Q: sin(t) х Suppose F(x) = dt. Use the Fundamental of Theorem of Calculus to calculate dx :(F(x')). 6+t…

A: Given

Q: sin 4x Find the Laplace transform of f(x) =

A:

Q: tant Differentiate f(t) = et f'(t) =

A: We are given a function: f(t) = tan(t)et

Q: sin z Differentiate y =

A:

Q: Find F′(x).

A: Fx=∫0sinxt dt=t32320sinx=23sinx32-032=23sinx32

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: We have to find directional derivative of f at a given point.

Q: Laplace of derivatives.

A:

Q: 1. Use the fundamental theorem of calculus part 1 to compute the derivative VI-t²dt. cos(z) dr

A:

Q: f(x) = cos x + 3, [0, 27], midpoint

A:

Q: I am studying for a quiz and do not understand a few of the concepts that will be covered on it. Can…

A: The fundamental theorem of calculus states that for a continuous real-valued function, f on a closed…

Q: 2. Function: y = 2 cos ( 2.5x +) 2n 3n 5n 3 4 6 0° 30° 45° 60° 90° 120° 135° 150° 180° 7n 11n 2n 6 4…

A: Let us find the amplitude, period and displacement of the given SHM in the next steps.

Q: f(t) = sin2(esin2(t))

A:

Q: Sin t/ 1+ cos t = 1-cos t/ sin t

A: The given equation to prove is: sint1+cost=1-costsint Use the trigonometric identity, 1-cos2t=sin2t

Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 17 tan Р(-18, 18); а %3D…

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A:

Q: a) Calculate a) b) Calculate the lineintegral F dr.

A: In this question, we find the value of a and the potential function. In part b) we use the potential…

Q: Find the directional derivative of f at P in the direction f(u, у, 2) — гу + 2?%; Р(5, —1, —3);…

A: In this question we will use basic of calculus i.e concept of directional derivative. We will simply…

Q: subseqvent displacement as a function of x ,t

A: In this problem, we need to find the displacement for the given initial and boundary value problem.

Q: Find the directional derivative of the function at the point P in the direction the unit vector u =…

A: Solution is given below:

Q: The sine and cosecant functions are continuous on their respective domain. O TRUE O FALSE A function…

A: Topic = Functions 1) TRUE 2) FALSE

Q: Find local and extreme values of f(x) = x + sin r, [0, T].

A: To find the local and extreme value of f(x) = x + sin x, [0, pi] f'(x) = 1+cos x f'(x) = 0 1+cos x =…

Q: Fundamental Theorem: Let f(x) = [ Jcos (In t)dt . Find the value of f'(æ). %3D

A:

Q: tan-(t) Given F(x) = dt, evaluate F(0) and F'(0). 1+sin(2x) 1+ et-1

A: It is givne that, F(x)=∫1+sin-1(2x)1tan-1(t)1+et-1dt ......................................... (1)…

Q: Find the directional derivative of the function f (r, y) at the point (6,-2) in the direction of =…

A: The given functions are f(x, y) = x/y f(x, y) = x3y +12x2 - 8y

Q: Laplace transform of  sin 2t+et sin t

A: Given that: Let f(t)=sin 2t + et.sin t

Q: joint pdf of two randor f(x, y) =

A: Note: As the question contains more than 3 subparts, first 3 questions will be solved. Please…

Q: A) Use the chain rule to find dt where wxty,x = sint + cost y cost- sint.

A: We will use chain rule to find the answer :)

Exponential Growth Model

The relation that represents an exponential function is: