4. (a) (i) Calculate (4 + 6i)².

Q: Find the first and second derivatives of the function. Check to see that your answers are reasonable…

A: Solution is here

Q: Vector A) Prove that: V × (F×G) = (GV)F- (FV)G+ F(VG) - G(V-F). m) Find all of the second…

A:

Q: Evaluate the six trigonometric functions (the unit circle). a) t= 5 corresponds to the point (x, y)…

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: The points A(3, 0, 1), B(2, 0, 2) and C(3, 1, k) form a triang area Determine the value(s) of k for…

A:

Q: dx 5. ≈ 16 x J dx – x2

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: + 1 -оу-х -oy=x2

A:

Q: . y = x2 and x2 = y

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: diades/3-V169 3. Construct a sign analysis for the second derivative function and then use it to…

A:

Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

A: Given ,  The population of a certain state is known to grow at a rate proportional to the number of…

Q: Find the one-sided limits of f(x). Step 2 of 2: Find lim_ f(x). X→-7+ Answer 4 Points f(x) = -7x - 3…

A:

Q: Find the angle of intersection between the equations f(x) = 3x and g(x) = 4 - x 2 in the first…

A: Given f(x)=3x, g(x)=4-x2.

Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim 20…

A:

Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: We need to choose correct option.

Q: 8 3) If f(x)= 2 (x-1)*, then f (2) (1) = Σ k=0 a) b) 2 c) 4 d1

A:

Q: 1. What is the value of Sin 3? 4 TT 2. What is the value of Tan 3

A:

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

A:

Q: Solve the following second order differential equation, clearly showing all calculation steps d²y dy…

A:

Q: (a) Write the parametric equations of the line obtained in example 1. (b) Provide the corresponding…

A: Explained below

Q: T -2 -1 4 3 2 - -3 1 3. From the above graph of y = f(x), find the following limits: (a) lim f(x) =…

A: (a)  limx→-4f(x)=2   (b)  limx→-3f(x)=-2   (c)  limx→-2f(x)=-3   (d)  limx→1f(x)=infinite

Q: your cimal places. Radioactive substance X starts with a mass of 20 g. The half-life of the…

A: Given problem:- Radioactive substance X starts with a mass of 20 g. The half-life of the substance…

Q: Find the first five non-zero terms of the Taylor series for f(x) = 1 3 Jo.[ + + + Written compactly,…

A: Use taylor series formula for the function

Q: Let D be the region enclosed by y = sin(x), y = cos(x), x = 0 and = . The volume of the solid formed…

A:

Q: Question 1 of 9 Calculate the future value of each of the following investments. Round the answers…

A: I am attaching image so that you understand each and every step.

Q: Let g(x)= log4 (13-5x). State the domain of g using set or interval notation. . State the range of g…

A: g(x)=log413-5x Given function g is unbounded when 13-5x=0⇒x=135 The equation of the vertical…

Q: 5. Find the Taylor expansion of f(x)=x² - 2x + 4 at x = 2.

A: To find the Taylor expansion of fx=x2-2x+4 at x=2.

Q: Calculate the are bounded by the curves: C. y = e2x and x - 2y + 5 = 0

A: Area

Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

A:

Q: 2- Evaluate the integrals in Exercises 7- 8- 9- In 9 Son 24/2 In 4 S dr [ 21 e ² dt ex/2 dx

A: To evaluate the given integrals.

Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

A:

Q: 2. The function g(z) is obtained by applying the following transformations to the function y=-8. A…

A: Given problem:- The function g(x) is obtained by applying the following transformations to the…

Q: If f(0) = -6, f'(0): = 3 S³ = x. f''(x) dx = = - 20, f(3) = 297 11 and f'(3) X 18 then: -49

A:

Q: find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = (4t − 1)3 ℒ{f(t)} =

A:

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

A:

Q: A ramp is inclined at 12° to the horizontal. A cart is pulled 8 m up the ramp by a force of 120 N,…

A:

Q: Find the directional derivative Duf (2,0) where, f(x, y) = xexy + y and u is the unit vector in the…

A:

Q: b) Use chain rule 1 y= LESANNE aretan u where u eª ue

A:

Q: Find the value of k for which the constant function (t) - =k is a solution of the differential…

A:

Q: Find the area of M. == Let M be the region bounded by the parabola y (0,2) (-2,0) 4 0 L N ရာ T c…

A: Given problem:- Find M be the region bounded by the parabola y=(-1/2)x2+2 and the line y = - x - 2 .

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x - 3y - 2…

A: Since you have posted multiple questions i can do first question in image as per our company…

Q: S tanx 1+ COS X JX

A: Given problem:-  ∫tan(x)dx/(1+cos4(x))

Q: Below is the graph of a polynomial function with real coefficients. All local extrema of the…

A: (a)The function is decreasing in the intervals: (-∞, 9),(-6, -3),(1, 5),(8,∞). (b) The function has…

Q: Set up the integral to find the area of M, using vertical ectangle. Let M be the region bounded by…

A:

Q: You are building a cylindrical barrel in which to put Dr. Brent so you can float him over Niagara…

A: Given problem:- You are building a cylindrical barrel in which to put Dr. Brent so you can float him…

Q: Question Find the average value of f(x) = - over the interval [0, 2]. Submit an exact answer using…

A: The objective is to find the average value of f(x).

Q: Consider the function Step 1 of 3: Find lim f(x). x--6- f(x) = x²2 + 12x + 22 19x + 100 if x < -6 if…

A: Given.

Q: The height y (in feet) of a ball thrown by a child is 1 y = -x² + 4x + 3 14 where is the horizontal…

A: Solution is here

Q: Consider the following graph. Step 2 of 2: Determine the x-coordinates of any inflection point(s) in…

A:

Q: The surface of the sun has dark areas known as sunspots that are cooler than the rest of the sun’s…

A: As per guidelines, we are going to solve only one problem. So please repost the other problems…

Q: Let f(x) be a function given by f(x) = (a) Prove whether f(x) is a Dirichlet function. (b) Find the…

A: Given