Let u be a differentiable function of r. Use the fact that |u| = Vu2 to prove that u'- u # 0. %3D dr

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A:

Q: Find the length of the curve, L. y² = 64 (x + 1)° , 0 0 L =

A:

Q: In y dy dx 1 xy 20.

A:

Q: A population of 460 bacterta Is Introduced Into a culture and grows in number according to the…

A:

Q: Calculate the taylor polynomialT3 Centered at X=a for the given function and values of a and…

A:

Q: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

A:

Q: Let logb A=3 and logb =-4. Find logb AB

A:

Q: Consider the following planes. -6x + y + z = 6 24x - 4y + 6z = 36 (a) Find the angle between the two…

A:

Q: 1 1-xl-x²-y? Evaluate the integral S S [dz dx dy 0 0 0

A: We will evaluate the given integral in this question.

Q: Limits allow us to move from the average rate of change over an interval to the (instantaneous) rate…

A:

Q: Use the chain rule to find the derivative of f(z) = 4/10z5 + 4x4 Type your answer without fractional…

A:

Q: The tangent line to the graph of y g(x) at the point (4, 2) passes through the point (1, 4). Find…

A: Tangent line to graph g(x) at a point (4,2)⇒(4,2) is point on g(x)g(4)=2

Q: Evaluate the following limit. (8x² -) lim (ху) - (6, -5) Select the correct choice below and, if…

A: In this question, we will find the limit of the function along two different paths .

Q: What values of x within [0,2pie] does f(x) = x-2cos(x) have a horizontal tangent line?

A: Given problem:- What values of x within [0,2pie] does f(x) = x-2 cos(x) have a horizontal tangent…

Q: EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION…

A:

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A:

Q: If the real part of an analytic function f(z) is x^2-y^2-y, then the imaginary part is О 2ху+x O 2xy…

A: We have to find the imaginary part.   According to our guidelines we can solve only one question so…

Q: Let R= [0,2]×[0,2]. The integral || xedA = e2 -3 R. Select one: O True False

A:

Q: Consider the following vector field. F(x, y, z) = 8xye²i + yze*k (a) Find the curl of the vector…

A:

Q: 4. Find and classify the critical points of a) f(x) = and b) g(x) = 3x³ – 5a3+ 1 5- 27.

A:

Q: Find Ax) if A1) =-5, and the tangent line at x has slope (3x- 1)e*-2*.

A: The tangent line at x has slope 3x-1e3x2-2x and f1=-e2

Q: Calculate the derivative: d dx * ST (6t3 – 9t) dt = -

A:

Q: a. y'=-20x (3– 5x')" 32. Suppose that x and y are both differentiable functions of t and are related…

A:

Q: Is the given series 1 + 4 2 - 1 + 12

A:

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y =…

A:

Q: If the limit of the sequence of partial sums of a series converges, so does the series. OTrue False

A: Given data

Q: a) obtained by rotating the curve Sketch and find the area of the surface y =/2x + 3 for x E [2,4].…

A:

Q: Consider the following vector field. F(x, y, z) = xy²z²i + x²yz²j + x?y²zk (a) Find the curl of the…

A:

Q: A. Using the definition of derivative, find the derivative of the follow function. 1) f(x) = ! 2)…

A:

Q: c)Test the series Ln =0 3n+1 for convergence or divergence.(write C or D) Answer:

A: This question can be solved by applying ratio test.

Q: If vector T = (x+ y+1)i+ j– (x +y)k then T.curl(T )is

A: We are given vector T.

Q: Question 4 Rolle's theorem states that if a function fis continuous on the closed interval [a, b]…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: (2x- 1)dx, n = 4 Calculate the Riemann sum of the integral using the given value of n.

A:

Q: You deposit $1000 in an account with an annual interest rate of r (in decimal form) compounded…

A:

Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

A:

Q: r(t) 12t i + 813/2 j + 3t² k, 0 < t<1

A: Here We have to find the length of the given curve.

Q: S |8:xydxdy y=-2 x=1

A: For the following problem,

Q: Given the power series 2 (-1)" x" n = 0 Find the Derivative of the Power Series. x (n + 1) d A 2…

A:

Q: Find. the Powier Series. and frad their Intervals and. sadif of. convergengeo If F(x)= g(x)= then…

A:

Q: SE-D) dx =- 4 In|x| +C 1. A. 4x В. 4* SA dx = 6Vĩ + c S(3Vx + dx = x + 3) + C 2. С. 4 3. D. -dx =…

A: Topic:- derivatives  Note:- as per our guideline if more than one question uploaded than only first…

Q: 10 Below is the graph of y = f(x). Find | f(x)dx. Round your answer to three decimal places. 5 10

A: Given:      ∫210fx dx   = Area under the curve between x=2 and x=10

Q: A particle moves in a straight line with velocity t-2 – * ft/s. Find the total displacement and…

A:

Q: 1. Which of the following series are power series? 3(х + 2)" In(n) (iii) (i) ::: 11 nx2n sin" (x) (x…

A:

Q: Calculate Hhe taylor polynomial Ta Centered at x=a for the iven function and alues of a and Estimate…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx? + y² + z? (2,…

A:

Q: 5 s2+ 3 s2 –8

A: Let's find.

Q: a) ) Sketch and find the area of the surface obtained by rotating the curve y=/3x+4 for x E [3,5).…

A:

Q: The series E=1 is convergent. 1+(" Select one: O True False

A: ∑n=1∞ 21+34n

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2* - x has a critical number…

A: Let's find.

Q: We say f : R –→ R is even if f(-x) = f(x) for all x. We say f is odd if f(-x) = -f(x) for all x. (a)…

A: