Find the limit of the vector-valued function if it exists. lim(e² i + sin(t)j + e¯¹²k) O does not exists Oi Oi+j+k Oi+k

Q: 3- Find the derivative of sinx +x/2+cos x.

A: A detailed solution is given below.

Q: Use the given graph of the function to find the function information. (A) Intercepts (B) Vertex (C)…

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Q: Find the surface area of the plane ( 15x-5z+20y=35) if it is in the first ? octant

A: Let's find surface area of given plane 15x-5z+20y=35 in the first octant.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: In this question we have to find the volume generated by rotating the region bounded by the given…

Q: 4 [*ƒ 2 [ (8f(x) 11g(x)) dx = Use the fact that [²ƒ(2) dz = f(z) = [₁ (81(x) - f(x) dx = 26 and 4 Lª…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let T be the triangular region with vertices (1,0,0), (0, 1, 0), and (0, 0, 1) oriented with…

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Q: find -1 2 5+1 s(5+1)²

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Q: dy Find given that dx cotx y² · log(x² + y²) = √√√+y√tan(x)

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Q: Question 5 Use Pascal's triangle to expand your binomial expression. A (1 + x)³ (1-x)³ (1 + x)4…

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Q: 2. Evaluate J dx x²√√x²-49) x>7, using a trigonometric substitution.

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute  take…

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Solve the following ff12 [2yx² + 2 sin(2x) + cos(πy)] dA, if R = [−2,1] × [0,1]

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Q: One number exceeds another by 1. The sum of the numbers is 73. What are the​ numbers?

A: Given data÷ One number exceeds another by 1. The sum of the numbers is 73.     Let assume that  One…

Q: Evaluate the integral. dx x216x + 65 NOTE: Enter the exact answer. + C

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Velocity is obtained by differentiating f(t)

Q: y =(3+5.x)" Use Logarithmic Differentiation to find dy da dy dx

A: topic- logarithmic differentiation

Q: 4.(2x³ -5x² + x)dx 5.[(5x² - 4x+2)dx

A: This is a problem related to integral of the function. Based on the general formula and concept we…

Q: Evaluate the following dx (x - 1)(x-2)(x-3) integral s

A: We need to evaluate integral.

Q: 10- Prove that a.b= la+bl²-la-bl²/4

A: solution:-a.b=a+b2-a-b24R.H.S=a+b2-a-b24=a2+b2+2a.b-a2+b2-2a.b4=a2+b2+2a.b-a2-b2+2a.b4=4a.b4=a.b=L.H…

Q: The height (feet) of an object launched in the air t seconds after launch is given by s= - 16t²…

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Q: The graph to the right is a graph of a polynomial function. (A) What is the minimum degree of a…

A: The objective of the question is determine minimum degree of the given graph of the polynomial and…

Q: Evaluate f sin √r dr

A: Topic = Integration

Q: Find the indefinite integral. f(e¹ i + j + costk) dt O ei + tj sint k O ei + tj + sint k O e¹i +…

A: We have to find the integral.

Q: Use limits to identify all the linear asymptotes of r³ - 3x - 1 x² f(x) = 2x² +1 x² + 2x +1' x < 0 x…

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Q: B) Find derivative of the following function d -6tanx dx

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Q: 1.) The height above the ground at which a ball is released at an initial height of 122.5m is given…

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Q: Find the area bounded by the graphs of y = cos x and y = y = x² y = = COS X 2 X

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Q: The radius of a circular oil spill after tt minutes is given by r(t)=√9tr(t)=9t. Find the…

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Q: Evaluate the following dx (x - 1)(x − 2)(x-3) integral s

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Q: dy dx || x3 2+y²

A: Given differential equation, dy/dx= x³/(2+y²) So, (2+y²)dy=x³dx

Q: Evaluate the following integral − (x - 1)(x-2)(x − 3) -

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Q: B- for the function below, the domain and the range is respectively -2+√1-x (-∞0,00) & [-2,00)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the limit. (If an answer does not exist, enter DNE.) lim x → 3 x2 − 8x + 12 x − 3

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Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A: We can solve the given problem by using the second derivative test.

Q: # dx -3 (sint) dt

A: We want to find derivative of the integral

Q: Use interval notation to write the solution set of the inequality. 2 x² + 3x-28≤0 The solution set…

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Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

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Q: Ex: Estimate the value of №.1.5 by..binamia.. sevies. Sol 4.5 = (1+015.) ². X=0.³.5 m = 0.15... 3 •:…

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Q: Write down the first five terms of the expansion of (1 + 3x)²/½/2 for /x/ < =//=

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Q: B- The derivative is y = ln (sec (In 0))

A: Solution ) y = ln (sec(ln θ)) Using chain rule  dy/dθ = (ln m/dm) × (dm/dn ) × (dn/dθ ) m = sec(ln θ…

Q: A- for the function below, the domain and the range is respectively y = |x|-2

A: Here we have to find the domain and range of the given function

Q: x Cos y Q7. Let f(x, y) = ye ²x + Find fxyx (0,1). √√y² +1 dy dz Q8. If z = x² + 3y, x = sint and t²…

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Q: slope the line that passes through the given points. point-slope form of the equation of the line.…

A: We will solve the problem.

Q: a. lim (3x - 5) x->-1 b.lim x² -9 xxxx²²-4x+3 2 x²-9 c.lim XX x² - 4x +3 2

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Q: 23 34 3- prove that w = ww if w = xy? + x³y³ + x'y³ W= ху ах' ду

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Q: 2.1-dx 3.J12x³dx

A: Here we use formula of integration.

Q: 4. Given the function y = 2x³ - 4x² + 5, find its derivative.

A: Differentiate with respect to x

Q: C-the derivative is y=0³ e 28 cos 50 e 20 (3cos 50-20 cos 50-50 sin20) it's 02e-20 (3cos 50-20 cos…

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Q: Show that the following DE are Bernouli type and solve: 1. y’ – x = y 2. s’+ 2s/t = s 3 t 4

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Q: Use a graphing calculator to find a linear regression model for the men's 100-meter freestyle data…

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