1. Use first principles to differentiate the following function. f(x)=2x(x-3)

Q: Question 1 A function z(x, y) of x and y is given by the formula z = r² sin(30), where r and 0 are…

A: We are given the function z(x,y)=r2sin⁡(3θ), where rrr and θ are polar coordinates.  Starting at…

Q: Which of the following is a solution of the initial value problem S 1 Sy ln(y) dx + x dy = 0 \y(e) =…

A: Step 1:  Step 2: Step 3: Step 4:

Q: Pls help ASAP. Pls show all work and steps.

A: IMAGE :

Q: If f(x)=(6/(6x2−4x−5)^3). Find f′(x

A: Step 1: Step 2: Step 3: Step 4:

Q: only part e needs an answer.

A: To find where the function f(x)=x4−9x3 is decreasing, we need to determine where its derivative,…

Q: Pls help ASAP. Pls show all work and steps. Pls circle the final answer.

A:

Q: Calculate f′(3) to 3 significant figures where f(t)=(2t^2+1t−4)^−8

A: We are tasked with calculating f′(3)  for the function:f(t)=(2t2+t−4)−8 1: Differentiate the…

Q: Let P be a point on the graph of y = x³. The tangent line at P will intersect the graph at the point…

A: Step 1:

Q: Pls help ASAP. Pls show all work and steps. Pls circle the final answer.

A: Let's solve each part of the problem using the information provided. Given Lines :The two lines are…

Q: Find the eigenvalues and eigenvectors of two following matrices

A: What are Eigenvalues and Eigenvectors?For a given square matrix A, an eigenvector v is a non-zero…

Q: Course Name: Calculus with Analytical Geometry-1 Course Code: MATH 132 Instruction: 1) Solution must…

A: The maximum height of the ball is given by the vertex of the parabola. The x-coordinate of the…

Q: Please help on all asked questions. Please show all work and steps. Pls circle the final answer.

A: Explanation :To find the points on the graph of y=7x/(x−2) where the slope of the tangent line is…

Q: (d) I = √2xy ds_where c is defined by the parametric equations x = 4 cos 0, y = 4 sin 0 between 0 =…

A: Step 1:The given integral is:I=∫C​2xydswhere the curve C is defined by the parametric equations…

Q: 44578.28  or 14184 π is the wrong answer for this question. I would like to try again for this…

A:

Q: 2. √√ x³ e* dx = x3 3x² 6x ex ox e. e. x 6 ex 0 ex

A: If you have any problem let me know in the comment section thank you.

Q: Sketch the graph of a function that satisfies all of the given conditions. f ′(x) > 0 for all x,…

A: Explanation:   f'(x) > 0 for all x: • This means the function is always increasing.  f''(x) >…

Q: Let S be the parabolic arch given by r(u, v) = (u+v, u−v, 4-u²) where (u, v) € [−2, 2]×[0, 1].…

A: Step 1: Step 2:Please give helpful rating Thank you  Step 3: Step 4:

Q: In Exercises 33-38, find the value of (fog)' at the given value of x. 33. f(u) = u³ + 1, u = g(x) =…

A:

Q: Solve and show formulas

A: Centroid of the region bounded by the curve y=4−x2 and the x-axis. The formula for the coordinates…

Q: Consider the second order linear differential equation (t+7) y″ − y' + t y Let y1(t) and y2(t) be…

A: Given Differential Equation(t+7)y′′−y′+ty=0 For a second-order linear differential equation of the…

Q: 8. [ √3 arctan x dx = 9. S 0 x²ex dx = Page 8 of 12

A: Step 1:Let u and v be two functions of x.Then the following formula of integration is…

Q: Q3. [5 marks] A potato at room temperature (20°) is put into an oven maintained at 100°. After 20…

A: Potato at 20 oC put in the oven at 100 oC for 20 minutes After 20 minutes, the potato is put in the…

Q: Please answer the given question with step by step working outs

A: In polar form, a complex number z is represented as r(cos θ + i sin θ), where r is the magnitude of…

Q: x+1 The function f is defined by f(x)= 1 Simplify lim f(x) using limit theorems. 1 x-0 X lim (x+1) X…

A: The function f(x) = (x+1)/(x-1) can be simplified using limit theorems to the following…

Q: 12. A rectangle with base along the x-axis is inscribed in the top half of the ellipse: x² +4y² = 4…

A: Let, L be the length of rectangleW be the width of rectangle Let, (x,y) be the point that connects…

Q: Show the following matrix is orthogonal and find whether it is a rotationand/or reflection and the…

A:

Q: Can someone please explain what is happening in the second line? How were they able to get that?

A: This is just a simple algebraic manipulation, just rearranging the  numerator in order to factor out…

Q: 1) y=x-2x² - 3 a) Finding all intercepts (Hint: Equation factors into (x² - 3)(x² + 1)! b) First…

A: b)Part d

Q: Pls help ASAP. Pls show all work and steps. Pls circle the final answer.

A: Step 1:Question 5: Plane through the Origin Perpendicular to the Given Line Step 2:Question 6: Line…

Q: Find the derivative of the function. h(x) = √1-x² sin-1(x) h'(x) = Need Help? Read It Submit Answer…

A:

Q: Smoothness of Virtue

A: For part (a), we need to sketch a function that is continuous everywhere but not differentiable at…

Q: Hi i need help with Derivatives of Hyperbolic functions.  How do I differentiate and simplify y =…

A: Step 1: Step 2: Step 3: Step 4:

Q: Consider the following limit: lim x→0 tan(x) X x3 A. What type of indeterminate form does the above…

A:

Q: Hi, I need help with an Inverse Hyperbolic Trig Function.  How do I differentiate and simplify y =…

A: Step 1: Identify the Function StructureThe function y=ecosh(3x) is a composite function. It consists…

Q: Which of the following is a solution of the initial value problem √ y ln(y) dx + x dy = 0 \y(e) = e…

A: ANSWER :​

Q: 4. Calculate d 1 dx Evaluate at x = 8.

A:

Q: The given function f(x) = = x+4 x²+4x if x-4 if x || -4 4 is continuous at x = -4. Write the…

A: Let's verify the three conditions for continuity of given function f(x) at x = -4:1. f(x) defined at…

Q: 2. [0/2.5 Points] DETAILS MY NOTES SCALC9M 3.7.008. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE…

A: Given that the area of the rectangle is constant and equal to 2,197 m², we can express y in terms of…

Q: Hi i need help with the problem that is in the attached image.  Thank you so much

A: Step 1:Step 2: Step 3: Step 4:

Q: Does there exist a function f that satisfies the following four properties simultaneously? • The…

A: Step 1:The problem asks for a functionf(x)that satisfies the following properties simultaneously: 1.…

Q: Please help on all asked questions, Pls show all work and steps, and circle the final answer.

A:

Q: Answer the given questions with step by step working outs

A: Question 3:Given:AB = 2aAC = -2a + 6bAD = 3bProof:For B, C, and D to be collinear, the vector BC…

Q: Use polar coordinates to find the volume the volume of the solid above the cone z = (x2 + y2)1/2 and…

A: Step 1: Formulas used    Step 2: Step 3: Step 4:

Q: answer it

A: 1.To find dxdy​ for the curve given by the equation:5x2+29xy+15y2=24We can use implicit…

Q: For what value of the constant a does the substitution u = ya converts the differential equation -t…

A:

Q: 4. S 1 x(x² + 4x+5) dx

A:

Q: Tafu is working with subatomic particles in the Physics lab. A positron is traveling in a straight…

A: Step 1:Step 2:

Q: Please help on all asked questions, Pls show all work and steps, and circle the final answer.

A: Step 1: Step 2: Step 3: Step 4:

Q: Use the Laplace transform to solve for the general solution y(t) of the system:x′ = 2y − ty′ = −x −…

A: Given :              x′=2y−t               y′=−x−3y+etwith initial condition  x(0)=0  and  y(0)=0…

Q: 9. (a) Find the points at which the function 1 f(x) = ·x² (6 − x). - attains a local maximum or…

A: