Hew-2 Find the directionat derivative of the funCtion X+XCos7-y Sinz +yat the faint Pe (2,=ly0 toward the Raint Pi los.

Q: Use the given graph of f over the interval (0, 6) to find the following. 1- 1 (a) The open intervals...

A: given :-  graph of f over the interval (0,6)  To see the interval where f is increasing.

Q: dy If y = sin='(cos x) then dx ||

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Q: Use the Second Derivative Test to find all local extrema, If the test applies. Otherwise, use the Fi...

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Q: dy then dx sin x If y = 1+ cos x ||

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Q: Find the vector component of v = (4, 7) along b = (2, 6, –9) and the vector component of v orthogona...

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Q: Consider the points A(3,-3, 3), B(4, -5, 1), C(-2,-4, 1), and D(6,3,-5). (a) Find the volume of the ...

A: Given: A(3,-3,3) ,B(4,-5,1) ,C(-2,-4,1) and D(6,3,-5)

Q: Let a=ci+j and b=3i+6j. Find c so that a and b are orthogonal.

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Q: Derivative of f(x)= 4x/5x^2-1

A: We can find the derivative as below.

Q: 0. You are constructing a cardboard box with the dimensions 50 m by 20 m (see the figure below). You...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: tind the deatNe of 2メー3 うメース the definition - ensing

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Q: Question 3 х? + ах — 2bх — 2ab - х3 -2ах?-2bх2 dx х4 + ах3 — 2bx3 - 2abx?

A: Let's find. 

Q: 的+十」 (8-9) = TT

A: To evaluate the given integral.

Q: 4 | a sin(3y+ x²)dydx, 2 a) Sketch the domain of integration on an (x,y)-plane. b) Set up the integr...

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Q: Find the following limit algebraically if it exists. Write DNE if the limit does not exist. Show all...

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Q: Integrals Involving Roots Evaluate each of the following integrals. 1. 2+Vx-4 xp-

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you wan...

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: 4. Find a polar equation for the curve represented by the Cartesian equation y = 3x. T = r cos 0, y ...

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Q: 1. Answer the following question? A Let f '(x) = x - 2x – 3. For what value(s) of x does f(x) have a...

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Q: A solid lies between two parallel planes 5 feet apart and has a volume of 45 cubic feet. What is the...

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Q: Consider the function: f (x) = x³ + 3x2 – 45x + 3 Step 1. Find the critical values of the function. ...

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Q: Haw Findd 32f 32年 and 32f |- Pcxxy) =tan'cx+y) woyg ズ mo は 2- fCx,y) xty + cosy +y Sinx. %3D

A: To find out the partial derivatives.  

Q: How-2 Find Zxx if Z =frusv),u = xy,V=2xy Ex PresF とhe anfwer in termo ofXッリZu, Zv

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Q: Find the solution of the following Differential Equations 2) y"+2y'+y x 4) y"+y=-30sin(4x)

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Q: Consider the points A(3, –3, 5), B(5, –5, 2), C(-1, –4, 2), and D(4,1, –8). (a) Find the volume of t...

A: The volume of the parallelepiped spanned by vectors a→, b →and c→ is given by a→×b→·c→ We know that ...

Q: Which of the following equations is an exact DE? O (10x^2 +5)dx-20xydy%3D0 O (2xy-3x^2)dx+(x^2-2y) d...

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Q: Find two unit vectors in 2-space that make an angle of 45° with 5i + 4j. NOTE: Enter the exact answe...

A: We have to find two unit vector as given in the question. 

Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact answe...

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Q: he points A(1,-2,4) and B(2,-4,1) cach make direction vectors with the point (Xo.Yo, Zo). The point ...

A: The Parametric equations of the line are the components of the vector equation , and have the form  ...

Q: arbitrary

A: We have to eliminate the arbitrary constants from the given  function

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x2 + ...

A: Given equations are:  x2+y2-6ax=0x+y=6a The small bounded region is rotating about the line x=0.

Q: Use the method above to find the distance from the point P(-3,1,7) to the line through A(1,1,0) and ...

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Q: Find the derivatives of the following: 1.) x* + 2y = 6x 2.) f(x) = (tan 5x) (x + 2)²

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Q: x²dx Evaluate x2Vx2 -4

A: We will evaluate the given integral ∫x2x2x2-4dx in the following step.

Q: 12 TT CoS + i sin + i sin 6.

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

Q: 4. If g(t) = et +e-i' then g'(t) is which of the following? 2et + 4e2t (A) e2t + 2+ e=2t 2et + 4e2t ...

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Q: 8. What is dx (x2+8)3 9. What is {(Sin (tan (x*)} dx dy 10. What (x -2x +5)6 dx =一

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Q: Use the Root Test to determine if the series converges or diverges (-1)"2* (-1)"2ñ zuć en? (2n2 – 1)...

A: Given problem:-

Q: 2. Let V be the volume of a cylinder with height 5 feet and radius r feet. If the cylinder expands a...

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Q: Solve it correctly Q)x^4 + x^2 +1=0

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Q: Find for the given function. dz? w= 10z2 ez dz 2)

A: Use dervative rule

Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –...

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Th...

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Q: Which of the following is true for the interval (2,0) for the graph of fAx) shown below? 5+ 4 3 -5 -...

A: This question can be answered by considering the slope of tangent at any two points in the given int...

Q: dx Evaluate J 2/4+x²

A:    ∫1x24+x2dxLet x=2 tan u.=∫secu4tan2udu=14·∫secutan2udu=14·∫cosusin2uduLet v=sin u.=14·∫1v2dv=14-1...

Q: Express the integral in terms of the variable u, but do not evaluate it. eS-4 dz; u = 5z – 4 NOTE: E...

A: ∫01 e5x-4dx  here change the variable x to u u = 5x -4 du/dx = 5 dx =du/5 limit is change from  if x...

Q: Find the volume generated by revolving bout the line x -1 the area bounded by (y + 2) = 4(x + 2) and...

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Q: У7" — 1)" (10.х n=0

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-2ax=0x+y=2a

Q: Find Is, Iy and I, for the area enclosed by the loop of y? = x²(2 – x) %3D

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Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan...

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