Find dy dx 21) tan y = eX + In 4x eX + 4 A) - sin² y хeх + 4 B) - xcot y

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: fast

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 10 — 0. - - %3D -…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: Find the area of the region inside the circle r = 30 sin 0 and outside the cardioid r = 10+ 10 sin…

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Q: The International Space Station orbits the Earth at a height of 250 miles. What is the height of the…

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Q: 4. Under the usual addition 47Z/2021Z .

A: A detailed solution is given below.

Q: Find the length of the curve of the graph of the indicated function. y = 4x3/2, between points (1,4)…

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Q: Consider the function f: R → R define by f(x) = a?x3 + x² with a a real constant , a + 0, We can…

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: topic- derivative of a function

Q: Evaluate the iterated integral. 1 2r y 8ry: dz dy dx

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Q: Find u + v, u – v, and 3u 5v. Then sketch each resultant vector. | u = (-4, 1), v = (3, -5) %3D (a)…

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Q: The shaded region between the graphs of 2x2 + 20 and y = 3x – 15 is displayed - - below in orange.…

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Q: Using appropriate substitution dx 4 (x+ 1)2 - is equal to -/4-(x+1)2 – sin- (*) + C the above…

A: Given problem:-

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: Sketch the region whose area is represented by the iterated integral. sinx dydx O un in x tan (x/2)…

A: Here is the solution:

Q: 1. Find the equation of the tangent line to the curve x = e', y = et at t = 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = t = 0 T(0) = N(0) =

A: Unit tangent and normal vector

Q: Find the four​ second-order partial derivatives for​ f(x, ​y)= 7x4y8 + 8x7y5 Fxx= Fyy= Fxy= Fyx=

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

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Q: Find the arc length in the second quadrant of the curve x23 + y23 2/3 = 9 from x = - 27 to x = – 1.…

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Q: Use finite approximation to estimate the area unde the graph of y = 5x² and above the graph of f(x)…

A: As per guidelines, I can answer maximum three subparts if a question. Since you have asked fot…

Q: Find T(t) and N(t) at the given point. r(t) = 3 cos(t)i + 3 sin(t)j + tk; t = T .2. NG) = .2

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Q: Consider the equation y" + ay' + by = f(x) the constants a and b are real and different from zero,…

A: The given problem is solved below in detail.

Q: Find the area (to three decimal places) bounded byf(x)=x^2e^x and q(x)=4-x^2

A: Given problem:- Find the area (to three decimal places) bounded byf(x)=x2 ex and q(x)=4-x2

Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: A. The slope of one line is 0.7743 and the inclination of another line is 64.38°. find the acute…

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Q: Solve the following differenti- d'y 3. +2y=e"; dx dx

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Q: A company's marginal cost function is where x is the number of units. Find the total cost of the…

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Q: Find V· (V × F), if F(x, y, z) = 7e2*i+9xe³j – e=k. V · (V × F)

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Q: Find the linear approximation at x = 0 to each of f(x) = (x + 1)², g(x) =1+ sin(2x) and h(x) = e2*.…

A: To find the linear approximation at x=0 to the given functions using the formula:…

Q: 40senz are solutions of the differential equation senr It's known that y1(x) 2(z) : 4z2y" + 4ry' +…

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Q: Evaluate the iterated integral. SS 5x= dy dz dz = 0 0 0

A: Integration is evaluated by integrating first y then x then z.

Q: Evaluate J xy dA¸ where Ris the region in y =x? 2 A 13/7 16/3 18 D) 20 B.

A: To find : ∬xydA where  R is the region of y=x2 and y=0

Q: 3 4. 7 8. PO 723 1225.78 1853 246762942.68 3246.963419.05 3509.59 3555.42 The table is given by…

A: ------------------------------------------------------------- dPdt=Pa-bP1P1-baP·dP=a·dT…

Q: 44. Find the derivative of loga u with respect to x. a. log u du/dx b. u du/ln a c. loga e/u d. log…

A: Given data÷

Q: In every sphere of radius r it is true that its volume V is given by V =ar³ , A snowball is melting…

A: volume of snowball (sphere);V=43πr3differentiating w.r.t. time t;dVdt=-4π3(3r2) drdtdVdt=-4πr2…

Q: Consider the function g: IR → R , g(x) = 3x* – 32x2, the function has a turning point (x,y) for: 4 O…

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Q: Find the relative maximum and minimum values. f(xy) = 4x - 2y?

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Q: Two functions are defined by f: x ax + I andg:x 4b **1, where a and b are constants. Given that f(a)…

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Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: Problem 6. The area A of a triangle is given by A=ac sin B, where B is the angle between sides a and…

A: Area of triangle, A=12acsinBa is increasing at 0.4 units/sc is decreasing at 0.8 units/sB is…

Q: The graph of a function y (=) is shown At which point is the following true (Only type the letter of…

A: Topic:-   calculus

Q: Evaluate the triple integral. zy sin(yz) dV , where G is the rectangular box defined by the…

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Q: 10 (5, 10 -x, x>5 x55 Use geometry to evaluate f(x) dx for f(x) = O 12.5 O 25 37.5 Cannot be found

A: Given that fx=5,x≤510−x,x>5 To evaluate ∫010fxdx

Q: Perform the indicated operation. Simplify if possible. b2 64 b+8 b+8

A: To simplify the given expression.

Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

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Q: Find the slope of the tangent line to the curve y = (1+4x)? at the point x = 2.

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Q: Evaluate the double integral f(r, 0) dA. -7 cos(0) r dr de 497 2 Sketch the region R. 7/2 A/2 6 2 4…

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