Simplify the complex number. Express your answer in a+ bi form and include each step necessary in simplifying. 1+3i 3-1

Q: convert csc x/ cos x to sec^2 x/ tan x

A:

Q: If f(x) = (x2 + 5x + 8)*, then f'(x) = f'(5) =

A:

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

A:

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) 2

A:

Q: sin $ 3 y cos*3 ydy

A: We have to solve above integral

Q: Evaluate the definite integral. Use a graphing utility to verify yourr result. (sin(x) – 3) dx Step…

A: To evaluate the given difinite integral. By using a graphing utility to verify your result.∫0πsinx-3…

Q: f(x)=x tan x с.

A:

Q: If f(x) = 4 Tln(x), find f'(x). %3D Find f'(2). Submit Question

A: Differentiation

Q: Find the work done by the force field F(x, y, z) = xyi+ yzj+xzk or a particle that moves along the…

A: Given: Fx,y,z=xyi+yzj+xzkr(t)=ti+t2j+t3k

Q: Which of the following equations is a homogenous DE? O (xy? + x)dx + (x²y- y)dy=D0 O (x- y)dx+ (3x+…

A:

Q: Solve the equation (2xy - tan y)dx + (x^2 - x (sec y)^2))dy = 0

A:

Q: 3.) S(1 – sin?xcos²x)²dx

A:

Q: P5: |V4- 9x?dx 4 –

A: Let's find.

Q: Match each graph type with its corresponding function.

A:

Q: -1 Su(u² + 3)! du

A: We need to solve integral.

Q: Instruction: Create 1 example problem about Area Region Bounded by Different curves. Write the…

A: This question can be solved using the concept of area bounded by curves.

Q: 5- y? = 4x (4, 4) y = 2x – 4 (1,-2) Using a horizontal element of area, the area of the shaded…

A: Here  we have to find the area of shaded region.

Q: 12. A force of 170 N is applied to move an object 90 m horizontally. If the force is directed 33°…

A:

Q: 6. Which of the following integrals cannot be evaluated using integration by parts? A. ſe-*sin2x dx…

A:

Q: Find the limit, If it exists. x- 1 lim X---

A:

Q: 2 2 2 2 4' 16' 64' 256' 1024

A:

Q: Step 1 To find the definite Integral 9 dx by the limit definition, divide the Interval [2, 7] Into n…

A: For the asked steps we can solve as follows.

Q: Find the length of the curve 7 (t) = (cos(3t), sin(3t), 2t) for – 8<t< 7 - Give your answer to two…

A:

Q: Evaluate the directional derivative Duf (3, 4) if ƒ (x,y) = /æ² + y² and u is the unit V vector in…

A:

Q: Indicate whether the given series converges or diverges. If it converges, find its sum. 00 17) E Wik…

A: Solved below

Q: Determine whether the sequence converges or diverges, and, if it converges, find lim an: n-00 12) an…

A:

Q: Determine whether F(x, y) = 2x²yi+ 8xy j is a conservative vector field. If so, find a potential…

A:

Q: f(x)= sin (x² +2x)

A:

Q: Q3/ Find the limits x*+x²-2 1. lim X-1 -1 Vx+2-1 2. lim X-1 x+1

A:

Q: 14. The f'(4) for y = v3x2 + 1

A:

Q: 1 dx x(x3000+1)

A:

Q: Find r'(t). r(t) = (tan(11t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

A: r(t)=((tan-1(11t))i+tcos(t)j-tkDIfferentiate w.r.t.…

Q: Integration of (sin(x) + cos(x)) e^x is ______________.

A:

Q: S V9x² + 64

A:

Q: Write the first four terms of {an}. n + 1 10) an 3n - 1

A:

Q: Evaluate the following Integrals: sin(4t) – 3 sin(2t)² dt 5 Vsech(4x) tan (4x) dx 1. 6. 7. sinh 3y…

A:

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A: Given : f(x,y,z)=9x2y+5z2   To Find : Conservative Vector field by finding it's gradient

Q: 5. IF sin@=5 =E and@inthe first quadrant, find cos

A: We have to find the cos angle

Q: IV. Suppose z is a function of r and y, and tan Vy² + x² 2e&y¸ Solve for az az and dy

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: y = 4 (2,4) A y = 2x x = 2 B y =x (0,0) Region A is bounded by the lines y= 2x, y= 4 and the y-axis.…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Solve the triangle. (Do not round until the final answer. Round angles to the nearest degree and…

A: sine and cosine rule

Q: 1) (-1)*- n² 2" n=1 a) Show that the series is convergent. Show All Your Work!

A:

Q: Use the chain rule to find the derivative of f(x) = 6/3x + 5x10 Type your answer without fractional…

A:

Q: Find an explicit formula for an. 1 1 4'9' 1 1 14) 1, 16' 25

A:

Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: Let F(x) = f(x*) and G(x) = (f(x)). You also know that a' = 5, f(@) = 3, f'(a) = 13, f () = 1 Then…

A:

Q: 6) Shared by the circles r = 2 and r = 4 sin 0

A:

Q: Find the area of the region bounded by the given curves. Show the computed areas of sections using a…

A:

Q: y cos x+sin y+y 0. Solve the following dx sin x+x cos y+x differntail equation 1.

A:

Q: Identify the function and interval which does not meet the conditions for applying the Mean Value…

A: We have to solve above question