Let r(t) = (t2, 1 - t, 4t). Calculate the derivative of r(t) a(t) at t = 4, assuming that a(4) = (9, -6,-2) and a'(4) = (-6, 5, -3) d. r(t) a(t)t-4 = dt

Q: Determine whether the following series converges or diverges If the series converges, determine the…

A: The given series is:…

Q: х2 — бх + 9 dx Убх — х2

A:

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A:

Q: Sllerch the graph of the 18r=4sine given polacequations

A: Given

Q: Graph the function. Show at least one period. 15) y = 2 sin (2ax - 3)

A: the graph for given function is attached below:

Q: 4-x Q3) Evaluate triple integral , S S* dz dx dy.

A:

Q: O E. The series converges for p> (Simplify your answer.)

A:

Q: Find the absolute extrema of the function on the closed interval. h(s) = [0, 2] S-3 minimum (s, h) =…

A:

Q: Question A 5-foot ladder is leaning against a wall. If we push the ladder toward the wall at a rate…

A: let x be the distance of bottom of ladder from the wall andy be the distance between top of the…

Q: Solve the D.E dy + (xy – xy²)dx = 0 %3D

A:

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-9,0,…

A:

Q: Find the distance between the parallel planes 10х — 5у — 52z — 26 — 0. 2х + у + 2 %3 0 and - - NOTE:…

A:

Q: Evaluate r(g(t)) using the Chain Rule: r(t) = (e', e", 4), g(t) = 2t + 5 %3D r(g(t)) = ( %3D

A:

Q: (-1)" x2n+1 En=0 (2n+1)! Given: sin x = for x ER Determine the exact value of the sum Σ (-1)"(2n +…

A:

Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 15у — 12z — 2 %3D 0 (a)…

A:

Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

A:

Q: 22n Σ (2л — 1)". - Vn² + 1 3 n=1 Use limit comparison test to show that the given power series is…

A: Solving

Q: Evaluate the following double integral over the region R. 7 x-y') dA; R= {(x,y): 0<xS1, -1sys1}…

A: Here we have to evaluate the given double integral over the region R .

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: (-1)" Given: power series > (x + 1)" 2n2 +5 n=1 Find the interval of convergence of the power…

A: To find the radius of convergence we will find first limn→∞an+1anthen equate it to less than 1

Q: Question A 13-foot ladder is leaning against a wall. If we pull the ladder the wall at a rate of 6…

A: topic - application of derivatives

Q: nd the derivative/s of the given item. Final answer should Find if yvx- 8 = xy + 2 %3D dx

A:

Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or divergent { an } n=1

A:

Q: (b) h(x) = v2x³ + 1

A: Topic = Derivative Only Question B is asked by student.

Q: Use the limit definition to compute the derivative of the function f(x) = Vx + 2 at x = 1. (Use…

A:

Q: given below, evaluate lim f(x) and lim x→-00 f(x) = -4x² + 2x +4 sin (9x) ses without bound, you…

A: We have to find the following conditions according to the given information

Q: 4. .2 + 2x) cos(2x) dx

A:

Q: Find the volume trapped below the cone z = Vx² + y² = r over the semicircular disk: 2.0 y r dr do…

A: We need to find volume.

Q: A firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue…

A:

Q: (-1)"n" sin" () Σ n 2n n=1

A:

Q: Problem 1 (а, Find the first partial derivatives of the function f(x, y) = x²yVy + 4y2. (b) fxyx of…

A: fxx,y = ∂f∂x  ;  fy(x,y) = ∂f∂y. fxyx(x,y) = ∂∂x∂∂y∂f∂x

Q: The side lengths for AABC below are a, b, and C. The height of AABC is h, Fill in the blanks using…

A:

Q: Let a = ci + jand b = 16i + 12j. Find c so that the angle between a and b is Round your answers to…

A:

Q: in hrit insider= 14cos6 out side re1-asG Find area insider= 4G5G out side ret-sG in hrat quarter -

A: The area inside r=1+cos θ and outside r=1-cos θ is:

Q: Find the second-order partial derivative fry (x,y) for the function, f(x, y) = 4x3 - 5x?y-3y + 9

A:

Q: х2 - бх + 9 V6x – x2 хр

A: Given problem:- ∫ (x2 -6x+9)/√(6x-x2) dx

Q: Given that x=t3+t and y=3/2t4+t2, find dy/dx, d2y/dx2, d3y/dx3

A:

Q: 24 3y7 ts dy

A:

Q: +0 (-1)"n" sin' Σ n 2n n=1

A:

Q: Suppose the demand for an item is given by the demand function,D(q)=−8q+580, where q is units sold…

A:

Q: 1.5 (3-x Evaluate the integral L* dy dx using polar coordinate

A:

Q: Appraximate the critical numbers of the function shown in the graph. Determine whether the function…

A:

Q: (-3)"(x – 2)" Vn+2 VI. Consider the power series > n=0 1. Use Limit Comparison Test to show that the…

A:

Q: Question For the function given below, which statements concerning Rolle's theorem are true? 4x + 3…

A:

Q: 1. Evaluate the integral. -1 (6х — 12) dx

A: To evaluate the given integral.∫3-16x-12 dx

Q: Simplify completely 4 Int dt using FTC-1. da e3z

A: This question can be solved using the concept of Fundamental Theorem of Calculus Part 1.

Q: What is the general solution of the system x − 2y + z = 3 2x − 3y + z = 8   Multiple choice…

A:

Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

A:

Q: 2. If a function f(x) is differentiable at x-a, then function f(x) is continuous at? А. X-а В. х-х…

A:

Q: Find the smallest number n of terms needed to obtain an approximation of the series 27ke-0.254² k=1…

A: