0 Given the piecewise function f(x) = 5-x 5-z What is f (4) ? Answer: f4 (4) = What is f¹ (4) ? Answer: f'(4) = Where is f discontinuous? Answer: f is discontinuous at x = 0 and at x = Where is f not differentiable? Answer: f is not differentiable at x = 0, at x = 4, and at x = x≤0 0

Q: x²-3 (x-1)² . Analyze and sketch the curve given by f(x)=- if y': 2(x-3) (x-1)³ 4(x-4) (x-1)* and…

A:

Q: Q.2-Solve the differential equation (answer three questions only) lo d. y""-6y" +12y' - 8y = 0

A:

Q: Given the table of values of the function below, what is its limit as x approaches -1? x -1.25…

A:

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

A:

Q: Find dy dx for sin(xy) + y³ = x² + 1 and use it to find the equation of the tangent line at the…

A: use differentiation for finding the equation of tangent line.

Q: Given w = xex + ln(x²yz3) Determine дш дх O дш дх δω дх ди дх дш дх = ex(1 - x) + = xẻ +1+ 11 N|X 2…

A:

Q: f(x) = 2²3 on (0, ∞) x+3

A:

Q: What is the equation of the curve that passes through the point (-2,3) and whose slope function is…

A: Integrating the slope equation gives the curve equation

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: Here we have to check the convergence of given integral

Q: Find all the local maxima, local minima, and saddle points of the function f(x,y) = x² + xy + y² +…

A:

Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

A:

Q: Write an equation describing the relationship of the given variables. y varies inversely as the cube…

A:

Q: Question 5 What is the limx→ [(ln(2x - 4)) - (ln(x+3))]? If your answer is a Whole Number Fraction…

A: limx-infinity [ln(2x-4)-ln(x+3)].

Q: Find the area under the graph of x = 4 - y² on the interval [0, 2]. -3 -2 -1 1 2 3 → 1 0 -1 16 3 16…

A:

Q: Differentiate the following functions. You do not need to simplify, but you must show all your work.…

A: Differentiation with steps need to be done.

Q: Find the second order partial derivatives, a'z for the following equation дхду z = x cos y - y cos x

A:

Q: Evaluate: lime 1-sin 8+cos 8 sin 20-cos 0

A:

Q: The value of a car depreciates exponentially after it is purchased. In other words, V(t) = 20(0.5)t…

A:

Q: b) Suppose to i that and V х-у Calculate the x and and y by and Jacobian ð (u, v) 2 (x, y) hence…

A: Suppose that x and y are related to u and v by…

Q: The area bounded by the lines x = 0, x = 2, x + y = 4, and x – y = 4 is revolved about  the line x =…

A: Given problem:- The area bounded by the lines x = 0, x = 2, x + y = 4, and x – y = 4 is revolved…

Q: Let f denote the function if x < 2; 1 f(x) = if x 2. Which of the following is true about f? Of is…

A:

Q: Given: f(x, y) = ln[1 + x siny] Find: 8² f(x,y) 8x² 2 sin y (1+xsin y)² ○ _ __ sin² y (1+zsin y)²…

A:

Q: Which of the following is TRUE about the function y domain is greater than 3 O as →→ 00, y → 0 x = 3…

A:

Q: What is the equation of the tangent line to the curve y=x^ +2x −x+8 where x = 1? y = 7x - 3 y = 7x…

A:

Q: A triangle is measured and two adjacent sides are found to be 3 inches and 4 inches long, with an…

A:

Q: Express the number as a ratio of integers. 3.898 3.898898898...

A: 3.898898898..... this can be written as  3.898898898..=3+ 0.898 + 0.000898 + 0.000000898 + .. ...  .…

Q: U dou U 3 cz³ Ox² x³y² 2 Z Oy + 3 x ³ yz

A: Given :u=x3y2z2+x3yz

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A:

Q: y = In x (x-5)ez-1

A:

Q: Given: xIn y + y²z + z² = 8 Find: дх дz -(x + 2y² z) y(y² + 2z) -y ln y x + 2y² z - In y у2 + 2z -у²…

A: Let's find derivative of given function.

Q: Give the solution for Product rule, quotient rule, general power rule 5 8-ax y = 8 + ax/

A: Here we have to use the product rule, quotient rule and general power rule.

Q: Given: f(x, y, z) = e¯ª sin(yz) Find: ² f(x, y, z) əyəx O z cos(yz) et O cos(yz) e O-ze-* cos(yz) O…

A:

Q: Find the area of the region bounded above by y = x2 + 8 and below by y = 4. 10- 4 2 X -10 8 6 4/-2…

A:

Q: y²-6x²y=-9x ; y' at (1,3)

A:

Q: √√√x if x1

A: Explanation of the answer is as follows

Q: Which of the following corresponds to the limx→4 (¹2) w when evaluated? 0 4 2

A: Here is the solution:

Q: Using the concept of the derivative of sin x, what is the antiderivative of sin x? -2 cos x + C 2…

A: We know that: ddx(cos x)=-sin x...(1)

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

A:

Q: A full tank consists of a hemisphere of radius 4 m surmounted by a circular cylinder of the same…

A:

Q: Using the graph of g(x) below, answer the following questions. a) Where is g′(x) > 0?     b) Where…

A:

Q: What is f 5√xdx? 3 f 5√√xdx = 5x² + C 2 3 f5√xdx = 10x² + C 3 f5√xdx = 5x² + C 3 [ 5vxdx= 5x? +C

A: Let's solve given integral.

Q: The graph of O the x-axis O the y-axis O None of these O the Origin y = = xe is symmetric with…

A: From the property of the odd function we observe that function is symmetric property.

Q: Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph of,…

A: To find the gradient of the tangent line of the point (5,1) on the graph of x+xy+2y2=12 Formulae…

Q: Evaluate: Express your answer in three decimal places. limx→8 √√x-2

A:

Q: Find the angle ? between the vectors. (Give your answer correct to 3 decimal places.) u = 7i − 9j +…

A:

Q: Calculate the iterated integral. 36 LTC + ar X dx

A: Solve the following

Q: 4.2.3. Find the integrating factor by inspection then solve the following differential equation.…

A:

Q: Use the Limit Definition of the Derivative to find f'(x) for the following function. You may NOT use…

A: Use limit definition to solve

Q: C. 6x³ +11x² - 4x -3/5 18x² +22x-4dx

A:

Q: Use the Integral Test to determine whether the series is convergent or divergent. nhe-n n = 1…

A: