Find the decomposition of a(t) a = aTT + ANN into tangential and normal components for r(t) = (3t, 3t², 3t³) at t = 1. (Use decimal notation. Give your answer to three decimal places.)

Q: If y = g(x) solves the initial value problem (IVP) Sy' = 4x + 12, y(0) = 20, and (x,y) is the…

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Q: Problem 3: Given the differential equation e* (e-* + e³) dx + ex (ex + 1) dy = 0: a. Identify…

A: We need to solve D.E.

Q: Given: y' +=(1-2x)y4 and y(0) = 1, Find C OA.0 B. 1 OC. 2 OD. 1/2 OE. None

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Q: - Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that…

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Q: Find the intervals where the function y = |a +11-1, whose graph is given below, is increasing and…

A: Given data:- The given function is, y=x+1-1

Q: You go to the doctor and he gives you 13 milligrams of radioactive dye. After 20 minutes, 8…

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Q: A closed cardboard box is constructed from different materials. If the material for the base of the…

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Q: Question 3 2y dx + x[x²ln(y)-1] dy = 0

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Q: 4x10 + 28x9 + 40x8 x11+ 2x10 Enter each answer as a comma-separated list of values. The order of the…

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Q: Give the following double integral containing general regions x + 3 ["S**³ 5 0 Find the value of the…

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Q: Consider the region R bounded by the curve y = sinx, the z-axis, and the lines = and x = Compute the…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first…

Q: Find the equation of the tangent line to the curve x² + y² + 2x + 1 = xy-8y at the point (-1,-9).

A: Given equation of the curve is  x²+y²+2x+1 = xy-8y We have to find the equation of tangent So slope…

Q: Problem 2: Given the differential equation (2xy - elnx-x²) dx + dy = 0: a. Identify whether the…

A: Given the differential equation 2xy-eln x-x2 dx+dy=0:a To identify whether the differential equation…

Q: Consider the function f(x) = 4x - cos(x) +5 on the interval 0≤x≤1. The Intermediate Value Theorem…

A: Given function:- fx=4x-cosx+5

Q: Given that; f(2)=2, f'(2)=3 g(2)-6, g'(2)=4 Calculate the following (fg) 2 = (f/g)'(2)= (g/f) (2)=

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Q: Define R as the region bounded by the functions f(x) = + 1 and g(x) = 2 between x = 2 and x = 3. If…

A: See this solution in below.

Q: symbolic notation and fractions where needed. Give your answer in the vector form.) t) = 1) = (7e² −…

A: See the details solution in below

Q: What is a suitable IF for solving the linear equation ty' + y = cost, t>0 3 OA. O B. OC. O D. O E.…

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Q: Given that; f(2)=2, f'(2)=3 g(2)=6, g'(2)=4 Calculate the following (fg)/2= (f/g)'(2)= (g/f)'(2)=

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Q: Given that; f(2)=2, f'(2)=3 g(2)=6, g'(2)=4 Calculate the following (fg)/2= (f/g)'(2)= (g/f)'(2)=

A: Please see the below picture for detailed solution.

Q: (x²y² + x² + y² + 1) dx + x² dy = 0

A: The given equation is  (x2y2+x2+y2+1)dx+x2dy=0

Q: Find the points on the surface x² - yz on the surface x² - yz = 5 that are closest to the origin.

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Q: One-inch radius steel ball bearings are machined so that the radius is within a tolerance of 20.004…

A: Determine the change in volume of a sphere dV if radius is changed by dr. V=43πr3dV=4πr2dr∆V≈4πr2∆r…

Q: (y4-2xy) dx + 3x²dy=0

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Q: (w³ + wz² − z dw + (z³ +w²z − w)dz = 0 3 3 - -

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Q: Convert the expression 4= 2048 into an expression involving logarithms. Then solve it.

A: The given expression is 4x=2048

Q: Find f'(9) if f(x) = 7x² +6x + 2 √x f'(9)=

A: we know, ddx(xn)=nx(n-1) for any real n

Q: Given: y' + y = y²(cosx - sinx)and y(0) = 2, Find C OA.0 OB. 1/4 O c. 1/2 OD. 3/4 OE. None

A: Let's solve given diffential and find constant C.

Q: Determine the required integrating factor: y dx + (2x+1-xy) dy=0 O x²e-x y²e-y xe ye -X

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Q: 8. If c is a critical number of f(x), then f '(c) = 0.

A: Given query is to find statment is true or false.

Q: Find dx (b) y = Do not simplify. (x - √e) sin-¹ (2x) √(5+ 2loga)9 (use logarithmic differentiation)

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Q: 1.) xy3dx + ex^2dy = 0

A: We need to find out the solution of the differential equation.

Q: 2y(x+y+2) dx + (y²−x² - 4x-1) dy = 0 ; y(0) = 1

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Q: Make a sign diagram for the derivative of the function. R) = -x + 4 = 4x + 5 F'(x) [ increase…

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Q: Given that; f(2)=2, f'(2)-3 g(2)=6, g'(2)=4 Calculate the following (fg) 2= (f/g)(2)= (g/f)'(2)=

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Q: Given: y' += (1 − 2x)yª and y(0) = 1, Find C 3 A. 0 B. 1 OC. 2 OD. 1/2 E. None

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Q: For this DE: . . (yetanx sec² x - 1) dx + etanx dy = 0: Check if it is separable, exact, or linear.…

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Q: Problem 1: Given the differential equation (x²y² + x² + y² + 1) dx + y² dy = 0 with the condition…

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Q: Use the given graph of the function to find the x-values for which f is discontinuous. Answer…

A: The graph of a function is said to be discontinuous at a point where there is a break in its graph.

Q: Rewrite csc 70 in terms of its cofunction cac 70°- (Type an exact answer Simplify your answer. Type…

A: topic- cofunction We are given , csc(79)°andcos2π7We know thatcsc(90-a)=sec(a)cos(90-a)=sin(a)

Q: 9. Determine the intersection (if any) of the following lines: F = (-8,-5,1) + t(1,4,-1) and F =…

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Q: Use the Chain Rule to find the indicated partial derivatives. z = x² + x²y, x = s + 2t - u, y =…

A: Determine the value of x=s+2t-u when s=2, t=5, and, u=3. x=s+2t-u=2+25-3=2+10-3=9 Determine the…

Q: Evaluate the following improper integral, showing all calculus and algebra work. Determine if the…

A: Given query is to find integral convertor diverging.

Q: Q3, If Pix)= 1x5 + x³ % gxXx) = h(x) = f(x) + g(x). Determine if hex) is even or add function. 1 3 R

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Q: 1 Σ(5) k Ξ

A: The given series ∑k=1∞-1k8k We have to find the convergence of the series.

Q: 3. Evaluate the following limits, if they exist. If the limit does not exist, write DNE x²+12x+20 a)…

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

Q: Question Find the derivative of the function f(x) = ln Select the correct answer below: 3 Xx O f'(x)…

A: The given function is; f(x)= ln[x3(2x+1)/(x2-3)].

Q: compare Exact and Non-Exact Differential Equation

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Q: Find all x-values where the function g(x): = 3x + 3sin(2x) has a horizontal tangent line. Select all…

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Q: How to get the derivative of the 7th root of (5+2logz)9?

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