Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx? + y² + z? (2, 7, 4) Vf(2, 7, 4) = Find the maximum value of the directional derivative at the given point.

Q: 4. A sawtooth wave is a kind of waveform that ramps upward and then drops off sharply. They are…

A: According to graph we see that  simpson's 1/3 rule is best method for accurate result .

Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

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

Q: Find the critical points of the following function. e* + e f(x) = - x

A:

Q: 元 |r' cos xdx

A: Solving the problem by finding the value of definite integral.   NOTE :: As per our Expert…

Q: 1. (-1)*z* (2k)! for |피 < ® COS I = for |피 < 0 Use the power series representations for cos r and e-…

A:

Q: i) The area of the surface obtained by the rotating the curve y=V 36-x, -3<x<3 about the x- | axis…

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

Q: Determine whether the (-1) "3" 00 geometric series * is convergent or n=1 6" divergent, and if it is…

A:

Q: If a, > 0 and -0 an is convergente then E(an)"2 is also convergente Select one: O True O False

A:

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

A:

Q: Find the third derivative of the function. f(x) =  5 x

A:

Q: Use the Laplace transform to solve the initial value problem y''+y'−2y=2e3t,y(0)=−1,y'(0)=4 y(t)=

A:

Q: 6.) r(t) = (cos t, sin t, In cos t), (1, 0, 0)

A:

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: Find two unit vectors orthogonal to a = (2, 5, 0) and b = (3,0, 5) Enter your answer so that the…

A:

Q: Show that the following diff erentia equation i s acomplete differential eguation Then find the…

A:

Q: Find the derivative of the function. y = 9 x + 3 y' =

A:

Q: Consider the following function. (If an answer does not exist, enter DNE.) Flx) = Vx² + 1 (a) Find…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: 48.x = 1, y = t², z = t³; (1, 1, 1)

A: This is a problem related to vector calculation. Based on the general formula of plane we will…

Q: Use implicit differentiation to find an equation of the tangent line to the graph of the equation at…

A:

Q: x²-3x-4 if x>-1 x- 4 if x < -1 10.Why is f(x) = %3D x-4 discontinuous at x = -1?

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: Find (f1)'(0). dt f(r) ((0) =

A:

Q: (2+In x)' 7.

A:

Q: Solve the differential equation. (t - 3)*s' + 5(t – 3)°s = t+3, t> 3 The solution is s= (Type an…

A:

Q: Find the area of the shaded region. r2 = sin(2theta)

A:

Q: f(x) = (x – 2)² 2. %3D

A:

Q: Test the series below for convergence using the Root Test. 3n 6n + 2 n=1 The limit of the root test…

A:

Q: Use the General Power Rule to find the derivative of the function. g(x) =    9 − 7x g'(x) =

A: We have to find g'(x) using the general power rule.

Q: Find the derivative of the function. y = 4t   t + 7 y' =

A:

Q: The average value of the function y = 10 x In(4 x) on the interval [3,7] is О 50.05 O 152.14 O…

A:

Q: 6. Which of the following is continuous at all points? B) f(x) = **+2x-35 ズ-5 xマ-4x-5 A) f(x) = x-5…

A:

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

A:

Q: A company invests $19,000 to produce a product that will sell for $56.85. Each unit costs $9.20 to…

A:

Q: tan 7x i) lim x+0 sin 3x sin(x2 + 3x + 2) j) lim x+2 x + 2

A:

Q: — т3 + 3х2 — 2х — 1. + 3x2 %3D

A: answer is in next step

Q: Find a general solution. Check your answer by substitution. ODES of this kind have important…

A:

Q: 12. r(t) at cos 3ti + b sin³tj + c cos't k =

A:

Q: First four terms of the sequence n²+3n 1+9 n are: None of them 2 10 9 28 5 19 14 37 2 10 41 28 5 19…

A:

Q: 8. According to the following table, what is the limit of this function as x approaches 0? -.001…

A:

Q: ! Consider the nonhomogeneous DE: y" + y' - 6y = (12 – 16x)e*. A) Verify that y, = 4xe* is a…

A:

Q: 2.25 † Let I" -a" if x + a, f(x) = I-a if x = a, where n e N. Find the value of e that makes f E…

A:

Q: Find the average value of the function LX TEX f (x) =4sin| on the interval [3,6]. COS 4

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: Find the derivative of the function. 6x3 f(x) = + 8x2 Step 1 The function (x) can be simplified to…

A: The differentiation is given below.

Q: n f(x) = 3x³ + 2x 5 verify that f(x) is invertible and, if so, find the equation of the tangent line…

A: Topic:- application of derivatives

Q: 6. Which of the following is the reason for a function differentiable at x=-5 if the function is…

A: Since this is a multiple question according to the Bartleby answering rule, only first question is…

Q: Determine the area of the region bounded. Show complete solutions. 1. y = 2x (1 – x), 0<x < 1

A:

Q: Consider the given: х3 — 4х2 x(х + 8)(х — 2) (x + 2)3 8(7x – 4) f(x) = ;f"(x) (x + 2)2 i f (x) : (x…

A: The given functions and their derivatives are: f(x)=x3-4x2(x+2)2=x2(x-4)(x+2)2,…

Q: Test the series below for convergence using the Root Test. n2n (In(n))" n=2 The limit of the root…

A: To solve thsi question we will apply the concept of root test and limit.

Q: Consider the surface defined by the equation z2 = 2x² + 4x - 6y? - 2y+ 1. %3D Find a set of…

A:

Q: n! 4) En=1 en 5)E cos(an) 2n=3 n Hint: cosan = -1,1,–1,1, .. n? 6) Ση-0 n+1

A:

Q: III. Graph the following functions: 4. y lIn(x-3) 5. y= In(x-1) 6. y= In Vx-1

A: Consider the functions 4.   y=|ln(x-3)|5.   y=lnx-126.   y=lnx-1