show that g(x) = (1/2)x has a unique fixed on [0,1]

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: Solve the initial value problem forr as a vector function of t. d'r - 2k dr? Differential equation:…

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Q: Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the…

A: We have to find the points and check the nature of function.

Q: Use the graph to find the following limits and function value for each value of a. i) lim f(x) i)…

A: Given query is to find indicated limits.

Q: Bolyng bernoulli differential equation

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Q: Solving Separable Equations: 1. dy - x-5 dx y2 2. = dx 3x²(1+ y?)

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Q: Q1) Use the Laplace Transform To Solve the Given Initial Value Problem: y +3 y + 2y = 4e' y (0) = 1,…

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Q: 9. (2xy – sec²x)dx + (x² + 2y)dy = 0 |

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Q: 3n². {(-1y"-1, 4n2 - 1 n-1

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Q: dy as a function of x. dx Write the following function in the form y = f(u) and u = g(x). Then find…

A: Given query is to find the derivative of the expression.

Q: Find the area of the region that is enclosed between y = 6x² – 2³ + ¤ and y = z² + 5z. The area is

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Q: 6. Two triangles can be formed using the given measurements. The other measurements of the triangle…

A: For other triangle m∠B=180-55.092=124.908°m∠C=180-124.908-41=14.092

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 20 and 5t, where a is…

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Q: he velocity vector? Di+O i+O k

A: Topic:- application of derivatives

Q: x+6 lim 2. X6 X -36

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Q: 14. %24

A: For determining the continuity of a function from its graph , we need to examine whether the graph…

Q: If 4x? + 5x + xy = 2 and y(2): – 12, find y'(2) by - implicit differentiation.

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Q: Given the function P(x) = (x – 1)²(x – 4) - -

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Q: 3. dt find F'(x) and F'(3) 1-2 17. Given F(x) =

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Q: What number is in the tenths place - 7.2431?

A: Given Number                           7.2431

Q: 4. Which of the following is the Maclaurin series fore Circle all that apply. (a) (b) (-1) (2n)! (d)…

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Q: 2) The height (in feet) of an object that has fallen for t seconds from a height of 800 feet is…

A: Topic:- calculus

Q: Write the composed trigonometric function sin (arctan x)sin (arctan x) in terms of x. Explain your…

A: In this question we have to find the function in terms of x.

Q: 2) Use the Chain Rule to express the second derivative of f •g in terms of the first and second…

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Q: The volume of the solid obtained by rotating the region enclosed by y = 30x - 6x, y = 0

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Q: (2x + ) dx + ( – 2y) dy = 0 12. (2х + 1+x?y², 1+x²y²

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Q: Find the number(s) b such that the average value of f(x) = 6x? 42x +70 on the interval 0, b is equal…

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Q: Write a in the form a = a-T+anN at the given value of t without finding Tand N. r(t) = (2t + 3)i +…

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Q: Find the following limit. Answer in either integer or fraction form. NO DECIMAL APPROXIMATIONS. If…

A: To find the limit.

Q: Find the slope of the tangent line to the curve below at the point (4, 7). 2x + 3y + /2xy =…

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Q: al squares fr ame if the pie 16

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Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= a(7- sin 0) and =7, where a…

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Q: G В R K + Match each equation with a graph above E 4(1.49)" a. blue (B) |- v |2(1.22)* b. orange (0)…

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Q: O Find the limit lim f(x). Select the correct choice below and, if necessary, fill in the answer box…

A: we have to find the limit

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: Q2 The following graph shows the position function r(t) of a mass attached to a spring. Note that…

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Q: For f(x) = 2x - 8x° +3 find the following. %3D (A) f'(x) (B) The slope of the graph of f at x = 1…

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Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

A: For a given vector v→, length of the vector is denoted by v→  and direction vector is obtained by…

Q: Construct a table and find the indicated limit. Vx +2 If h(x)= then find lim h(x). X-4 X-4 Complete…

A: To find the limit of given function as x approaches to 4

Q: #3) Rewrite the integral 27 .2 p dr d0 0. in rectangular coordinates.

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Q: f'(x)=-+e2* +x² and S(1) =. Find f(x) Given %3D

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Q: Evaluate the limit In(x) lim x+1 x2 - 19x+ 18 a. 1 19 O b. 19 C. 1 17 O d. None of these. е. —17

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Q: Write a in the form a = a-T+a,N at the given value of t without finding Tand N. r(t) = (3e'cos t)i+…

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Q: In n Consider the series Verify that the hypotheses of the Integral Test hold, and n2 n=1 use the…

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Q: Assume Za is opposite side a, 2B is opposite side b, and Zy is opposite side c. Solve triangle ABC…

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Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

A: A detailed solution is given below.

Q: Find the Taylor series of  f(x)=ln(2+x) around the point x=-1 by reaching the term n=4

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Q: 00 Determine whether the series omverges absolutely, conditionally, or n=1 not at all.

A: The given series is ∑n=1∞-1n-1nn2+1. A series ∑n=1∞un   is absolutely convergent if ∑nun  is…

Q: Find the velocity and acceleration vectors in terms of u, and ug. do r= 6 e a0 and -= 3 dt Ju, +Juo

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Q: Find T, N, and k for the space curve, where t>0. r(t) = (5 cos t+ 5t sin t)i + (5 sin t- 5t cos t)j…

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