Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0). (a)(E - ) (-i+2j) (b) V2 (-i-2) (c) (-i+)) (d) O a

Q: Find the point D'4, symmetric of D4 with respect to the line F4B1. F4: (-2,1,3) D4: (1,2,3) B1:…

A: Here we will find poinr D'4 symmetric of D4

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

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Q: f:(-2,1]→[0,12] literal and overlapping function 12 if įs(x) dx = 13andſls*(x) đx =5 [f*(x) dx=? 10

A: Given :f:-2,1→0,12 literal and overlapping function.∫-21fxdx=13     →1∫06f-1xdx=5    →2To…

Q: a) (3xy - y' + 2x) dx + (2xy 3xy + 1) dy = 0, y(- 2) = b) (ye* + 2e* + y²) dx + (e* + 2xy) dy = 0,…

A: A differential equation of the form M dx+N dy=0 is said to be an exact differential equation if it…

Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

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Q: For the linear operator L = D^2 −4D + 8, determine L(y) for y = e^(2t), y = e^(2t)sin(2t), and y =…

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Q: f(x)= x2/5 Where it concave up/down?

A: To find the concavity of the given function.

Q: س1/ حل التكامل التالي dx (x + 2) Vx2 + 4x+ 3

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Q: poin If g(u) —D V9u + 3 then g' (u) =

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Q: Q4) Consider the function f(x)= x³ -7x+3=0. Use Newton Method, find the positive root of…

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Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: 4 Suppose that f'(x) = 2x for all x a) Find f(5) if f(0) = 0. b) Find f(5) if f(4) = 14. c) Find…

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Q: let f(2)=3, f'(2)=4,g(2)=3,g'(3)=2. find (g o f)'(2)

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Q: se-2s -)=D 's²+45+3

A: Given,

Q: H (x) = VI-Soe? 2. %3D (f09) (><)= H (sc) %3D %3D 9(36) =

A: Given fgx=1-5x2

Q: Sketch the direction field of the DE y'=2x+y.  (Plot 9 or more points) Then sketch approximate…

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Q: (a) y'=ty (3-y), (b) y'=y (3-ty), (c) y'= -y (3-ty), (d) y'=t-1-y², y(0) = yo y(0) = yo y(0) = yo…

A: We will be graphing the slope field of the given differential equation along with the interpretation…

Q: For the generating function A(z)=- find the corresponding r≥ 0. 1-9z

A: Given: The function generating function is Az=21-9z2. To find: The numeric function corresponds to…

Q: find f

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Q: (2,–2), (4,4), (5,3) by a CUDIC SPime. 4. Determine constants a, b, c, d and e that will produce a…

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Q: f(z)=ze^tz/z^2+1 for this function find the Rez(f(z),i) and Rez(f(z),-i) .

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Q: Evaluate L{t cosh 4t. 1 1 + (s – 1)’' (s+1)* А. В. (s-1)* (s+1)* 1 1 С. (s –4)° (s+4)' 3. D. (s-4)*…

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Q: v (m/sec) 0 A 2 3 4 6 →t (sec) -2/ f(x)dx

A: Solution:Given       for x=5  y=0and x=3     y=2f(x)=5-xTo find∫35f(x)dx=?

Q: 2. +x +1 d

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Q: Let f(u)=u^3 and g(x)=u=6x^4+2. Find (f o g)'(1).

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Q: Let F = (t + 4) i +² sin(41) j+ t^k, G = e' i+ 4f* cos(t) j+ e$t* k and 512 -i+ 4² j+te²ª k 1 +t H =…

A: Given :  F=(t+4)i+t^ 2 sin(4t)j+t^ 4 k G=e^ t i+4t^ 4 cos(t)j+e^ 5t^ 2  H = (t ^ 5)/(1 + t) * i + 4t…

Q: y'= (6x-2y-3)10 When 9polyg the vavable change u= - 6x-2y-3 the eqn converts 'into? Oa du = (-2u" +…

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Q: 1. Let F(x, y, z)=x²+4x2+2yz². What is the direction of fastest decrease of Fat (1,2,-1)? (a) (b)…

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Q: F(x) = Vt² + 11 dt

A: F(x)=∫5xt2+11 dt

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: