Given the function f(x) = x2 and the closed interval [0, 1, which of the following is a value of c in the closed interval such that f(c) = +? 14 1/2

Q: Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i+8 sin(8t)j+ 5tk…

A: The given formula is: κt=r't×r''tr't3 And rt=8cos8ti+8sin8tj+5tk

Q: If we apply Rolle's Theorem to the function f(x) = 2x2 – 16x – 4 on the interval [2, 6], how many…

A: We state Rolle's theorem here ------    Let f : [a,b] -> R be a function continuous on [a,b] and…

Q: If a rock is dropped from a height of 193 ft, its poistiont seconds after it is dropped until it…

A:

Q: Evaluate the definite integral (cos(t), sin(t))dt

A:

Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

A:

Q: The function f(x) = 2+ 6x + 150x- has one local minimum and one local maximum. This function has a…

A:

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A:

Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

A:

Q: II. MULTIPLE CHOICE: Choose the correct alternative that satisfies the given question. Write your…

A: We have to find correct option for the given questions.

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

A:

Q: Double USA, manufacture of the Nicolas cage pillow has determined that the marginal daily revenue…

A:

Q: Solve the following differential equations of dy 1 y= xy': + dx

A:

Q: 19. What is the seсond derivative of y бх* - 3x1 + х2 -57 а. у 24х1 — 9х2 + 2х b. у"3 144х — 18 с.…

A:

Q: (y – x) dx + 15x?y? dy

A: answer is in next step

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

A:

Q: Evaluate lim,-(-- 7 - 10 + 4) | 4x3 O +∞ O -7 O -10 8.

A:

Q: Let h(x)= f(g(x)) where f(x)=tanx. Then h'(x)= a) f'(tan x) g'(x) b) g'(x)tan(g(x)) c) g(x)…

A:

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

A:

Q: 22 r = 7 sin 0 + 50 cos O

A:

Q: Consider the function f (x, y)=-2x'+3x'y+2 y°-9y+5

A:

Q: use the definition of the derivative to compute f'(x) given f(x) 3x+2

A:

Q: ||r(1) × r"(t)|| Use the formula «(t) to find «(t). r(t) = 11 cos(t)i + 11 sin(t)j + 6tk K(t) =

A: We can solve as follows

Q: 4- part 1 Find the derivative of the function f(u) = 4u° 4 - 2u1.8 0.4 %3D = (n),1

A: Differentiate wrt u

Q: Evaluate: Lī 3sin13 xda 512 1001 1024 1001 1024 1001 512 1001

A: Solved below.

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: The function f(x) = - 2a3 + 36x2 192x + 8 has one local minimum and one local maximum. This function…

A:

Q: Find a particular solution of the DE: y" – 6y' + 8y = 64x?. C. yp = 8x + 12x + 7 E. None A. Yp = 4x?…

A: Solve it

Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

A:

Q: S 289 xe

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 2…

A: Given problem:-

Q: Find the first four nonzero terms in the Maclaurin series for f(x). f(x) = e 5x sin x ... Choose the…

A:

Q: Consider the following equations. f(y) %3D У(5 — у) g(y) = -y

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 3 r(t) = 11 cos(4t)i+ 11 sin(4t)j+ tk K(t) =

A:

Q: Without solving for the undetermined coefficients, find the correct form of a particular solution…

A:

Q: Evaluate -5x lim,→0 tan x O -5 O 1 O 5

A:

Q: (a) Prove that the series Vn + 2x - Vn +x Σ n=

A: answer is in next step

Q: Let S be given by x? + y? + z² = 25 and z > 0, oriented downward. (a) Sketch S and dS. Indicate…

A:

Q: Find V · (V × F), if F(x, y, z) = 2e"*i+4xe"j – 4c*k. V · (V × F) =

A:

Q: sin (xexz +3y5+3x"-x 3

A:

Q: Use Green's theorem to evaluate F• dr. (Check the orientation of the curve before applying the…

A:

Q: dx Ух — 12

A:

Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…

Q: Find curl(2: i + 3x j + 6y k). curl(2: i + 3x j + 6y k) = ( )i + ( j + ( )k

A:

Q: Describe the graph of the equation. r = 2 sin 10t i + 2 cos 10t j O It is a circle of radius 10 in…

A:

Q: II P. Do Homework -Homework Chapter 4- part 1-Google Chrome…

A: Given query is to find the point where slope of tangent to the curve is zero.

Q: Draw a graph that does not pass through -8 and 8. Identify 3 points that is continuous at that…

A: Solve the following

Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

A:

Q: The velocity function of a moving particle on a coordinate line is v(t) = t2 + 3t − 10 for 0 ≤ t ≤…

A:

Q: Use the Divergence Theorem to calculate the surface integral F• ds; that is, calculate the flux of F…

A: