Find the area enclosed by the given curves (using applications of definite integrals).

Q: dx Ifz = x + y = -2, dt dy = 3, and z> 0, find dt dz at (x, y) = (4, 0). dt Please give an exact…

A: We know that derivatives power rule is  d(xn)/dx = nxn-1 Here i attached the solution of this…

Q: a+sinx If the function f(x) is continuous at x-0, then a = 2+2acosx x<0

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Q: Question 5 Determine the magnitude of the com

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Q: Find the vector component of v = (4, – 1,7) along b = (2, 6, –9) and the vector component of v…

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Q: Siven f(x, y) = 4e3" sin(3y) hen Vf(0,5) = 2 Question Help: DVideo MMessage instructor Add Work…

A: Given query is to find indicated derivative

Q: „T7/8 6) (1 + etan 2x) sec² 2x dx 16) B) - D A) e C) 2e

A: Given query is to find the value of the integral.

Q: 4x+10 J (x-2)(x²-2x+1)

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Q: Solve the differential equation. dP 3 Р(4) — 20 dx Using sqrt{t} for Vt. P(t)= 6sqrt{t} +8 O P(t)=…

A: Given query is to solve the differential equation.

Q: Vectors v and w have magnitudes ||ö|| = 2 and ||w|| = 8 and the angle between these vecto What is…

A: Given query is to find the dot product of v and w.

Q: Simplify f and find any vertical asymptotes of f. x²(x+8) f (x)= x²+ 8x

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Q: Find the center (h, k) and the radius r of the circle 4x2 + x + 4y? + y – 10 = 0.

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Q: Find the vector component of v = 2i – j+ 3k along b = i+ 4j + 8k and the vector component of v…

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Q: Find the tangent plane to the equation z = 7e. 4y at the point (8, 16, 7) = Z Question Help: D Video…

A: Given z=fx,y=7ex2-4y        Point x0,y0,z0=8,16,7 To find the tangent plane:

Q: sinh x 1+ cosh x

A: sinh x1+cosh x

Q: lim e 0 t/ Select one True False

A: limx→0+e1xusing chain rulelet f(x) =1xg(u) =eulimx→0+ f(x) = limx→0+ 1x =∞

Q: If −8cos2θ−4=−12, where 0≤θ<2π, what are the values of θ?

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Q: Qz IF A-(-2 4) B=(% 4) 2 3 -2 4 Prove! CA *B)*C A*(BaC)

A: Here, the given matrices are: A=-24, B=5104, C=23-1-241

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find the net area and the area of the region bounded by y 2cosx and the x-axis between x = - and x =…

A: Use the integration to find the net area and area bounded by the given region.

Q: x dx (7x2 + 3)

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Q: Apply region based segmentation for the sequence: F={7,5,9,1,10,2,9,12,4,11,3,17,16,19,15}…

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Q: Exercises

A: The given figures are: and

Q: 12) (sin (4x - 9) dx

A: Given function : sin (4x -9) To find : Integral of the function.

Q: In a certain environment, a colony of bacteria grows according to the model A = A0e^0.06t, where A…

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Q: esin 2x [In (cos 2x)]?

A: Given: fx=esin2xlncos2x2   As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Chain rule:…

Q: ee) Using the Laplace transforms to solve the following equations: y" + 3y' + 2y = e', y (0) = 0, y'…

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Q: 10 cm 10 cm 10cm

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Q: Find 3x? arctan x dx.

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Q: 7. * In [In (In æ)]

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Q: 2. A small business owner creates and sells x bars of handmade soap per month. The monthly profit…

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Q: Solve the initial value problem. - + 4y = 7, y(0) = 1 dt The solution is y = O

A: Given query is to find the solution of the differential equation.

Q: do number 3

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Q: A box with a square base and open top must have a volume of 13,500 cm. Find the dimensions of the…

A: Given query is to find the sides of the box

Q: 10

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Q: 4. How many fixed points does the function T(x) = tan(x) have? %3D

A: for fixed point f(x) = x x = tan(x)

Q: Consider the following. 1 ifx = if x = 1 x²- 1 F(x) =

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Q: Find the fifth term of the geometric sequence from the given information. Express the term as an…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ – y³, P(10,…

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Q: Let a = (4, – 5, – 4) and b = (4, 3, k). Find k so that ā and b will be orthogonal. k =

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Q: (2x – 1,x < 0 a,x = 0 0. Let f(x) = x+b Find, if any, a and b such that fhas limit for all x but not…

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Q: A2. If y = In10 10* then y'= %3D (a) x. 10*-1 (b) x10. In10 (c) 1 L 10* Ina

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Q: If a = (3, –3, –10) and b = (-8, –4, –10) find a · b =

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Q: Evaluate the limit below. 36 – x2 - 6 lim 5x

A: We have to evaluate the limit                                                limx→036-x2-65x

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question can be solved using the concept of equation of line in 3D geometry.

Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Given query is to find the average height

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: O Find all velues of sx for whEu tue serics Converjes. for these alues of l, wnte tue sum of tue…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: f(t) = -16t2 +385t +8 avg height from t = 5 to9.7 second f(9.7) =-16(9.7)2 +385(9.7) +8…