iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric equations of the tangent line to the graph of R(t) at t = 0.

Q: Determine if the function √x² + y² +1 x² + y² f(x, y): 1 2 is continuous at (x, y) = (0,0). If not,…

A: To find whether the given function is continuous or not at(0,0).

Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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

A:

Q: 16. Let lim f(x) = -7, then what is lim (-9. f(x))? X-C A. - 16 C. 16 D. 63 B.-5

A: limit

Q: Using trigonometric substitution to solve x-2√4 – x²dx = f f (0)d0. What is (a − b + ²)? A B U D I…

A:

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

A: We first graph x2+y2-6y=0 and y=6-x using a graphing calculator.  The shaded region will rotate…

Q: [₂7-4x dx -2 Determine the value of [4f(x) dx given that [ƒ(x) dx = 10 and ſº ƒ (x) dx = 3. 27 sin…

A:

Q: ปืน น g-x) (2+x) (4x - 42.Sou 1-2

A: Given:        π∫-228-x2-2+x2dx     =π∫-2264+x2-16x-4+x4+4x2dx     =π∫-2264+x2-16x-4+x4+4x2dx…

Q: Consider vector v = (1,2,2), point A(2,5,4) and point B(-1,5,1) - In center-radius form, find an…

A:

Q: √√7 - t³, cos t³) t³, c 3 R(t) = (sin t³,-

A:

Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A:

Q: Given x = - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8

A:

Q: 10 Determine the area above f(x)=x²+2x+3 and below the line y=11.

A:

Q: ND THE AREA BOUNDED BY THE = x(x-1)², y-AXIS, AND THE =12

A:

Q: dy Find the complete solution of 2e-2 cosx-sin²x = 0. dx Note: [e"du=e" + C

A: The given differential equation is 2e-2y cos x-dydx sin2x=0⇒dydx sin2x=2e-2y cos x⇒dy2e-2y= cos x…

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

A:

Q: y = (x² + 2)(x-3)

A: The objective is to find the derivative.

Q: d dx A.sinh(Inx) B.–sinh(Inx) sinh(Inx) C.- X -cosh(x) D. X cosh (Inx) =

A:

Q: Consider the vector-valued function R(t) = (t³-t, 2t², 2 - 21²). 1. Find ||'(t)||. (Simplify your…

A:

Q: 3 S₁² √(√²-√²)³ at dt

A: Using substitution method, integration is solved.

Q: (a) Find the exact area under the curve y = 1/x³ from x = 1 to x = t for t = 10, 100, and 1000. t =…

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: = 0 and y 16k (x-3) = 0. Find the area bounded by the parabolas (x - 3)² - 16ky =

A: Given: (x−3)2−16ky=0 and y2−16k(x−3)=0 Graph of the given curves will be as follows

Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

A:

Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A:

Q: z²√(-z² + 1)5 dz

A:

Q: 26 Find the value of k so that line 4, 2]-[2-20]++ [2, k₁-3) is parallel to the Plane *x+24-42=12

A:

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

A:

Q: Find a particular solution of =(x−1)² if y=-21 when x=-3. dx

A: dydx  = ( x - 1 )2   , y = -21, x = -3 we have to find particular solution of it

Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with…

A:

Q: Pls show complete solution (c) Set up the integral which yields the area of the indicated region R…

A: We need to setup integral for area.

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

A:

Q: The rational expression A TRUE B FALSE 1 (9x² +16)² can still be decomposed.

A: this can not be decomposed. This statement is false.

Q: In the quadratic equation Ax2+BX+C =0, describe the roots when B2-4AC is positive. The roots are…

A: The given quadratic equation is Ax2+Bx+C=0

Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

A:

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

A: We have to find the volume.

Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

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Q: Convert the Cartesian coordinate (-1,-3) to polar coordinates, 0≤ 0 0 r = 0 =

A:

Q: 39 9. A curve with polar equation r = 6sin0+13cose represents a line. This line has a Cartesian…

A:

Q: In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Let's find initially present bacteria.

Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

A:

Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

Q: example of properties of definite integral

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Q: rve (y+1)2 = 4x3 from x=0 to x=1? (4) =q8

A:

Q: Find the volume of R using shell method, when R is bounded by y = 4x - x², y = 0 about the line x =…

A:

Q: Find the equation of the tangent line to the graph of the function f (x) = sin (7√) at the point…

A: Here we have to find the equation of the tangent line of the function…