Find the limit. NOTE: Enter the answer using round brackets. t2 +8 1 lim t+oo\ 5t2 + 6' 8t (?, ?) .....

Q: 4. Using logarithmic differentiation, or otherwise, find the derivative of y = (sin r)".

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Q: Differentiate the following functions: 1) f (x) = 5 2) f (x) = -2x 3) ƒ (x) = -2x + 2 -2r +2 %D

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The sum of one number and five times the second number is 50. A. What are the numbers so that their…

A: Let the first number be 'x' second number be 'y'. A/q  x+5y=50⇒5y=50-x⇒y=50-x5 The product of first…

Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

A: We need to find speed at given point.

Q: 6. lim (sinx)*

A: u =eln u, then:limx→0+  (sin x)x  =limx→0+  ex ln(sinx)=limx→0+  eln(sinx)1x=elimx→0+  ln sin(x)1x

Q: Find the Taylor series for f centered at 9 if p(n)(9) = _(-1)"n! 7"(n + 1) (-1)" (x – 9)" 7" (n + 1)…

A:

Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

A: Given problem:-  A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = 8 cos(8t)i+ 8 sin(8t)j + 5tk…

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Q: 2) 2x2 csck) dy %3D CS )ゾー XeJx-2 メ-2

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s t s 1. (y - x) dx +…

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Q: 2) Find and of the following equation then simplify whenever possible. dx² x = Cos ß + Sin ß y = Sin…

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Q: Find V · (V × F), if F(x, y, z) = 5e²i+ 5xe®j– 7ev²k. %3D V ·(V × F) =

A: We know divergence of curl of any vector v is always zero.

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1,1).…

A: Given

Q: Find the area bounded by the curve y = 9 - x2 and the x-axis. a) Horizontal Strip b) Vertical Strip

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Q: Use the formula «(t) = F () ×F (51 to find k(t). ||r(t)||* r(t) = t²i+t°j K(t) = %3D

A: We have t find κ(t) for the given vector r(t) = t2i + t5j The given formula is κ(t) =…

Q: each of the following functions determine dr

A: Given query is to find the derivative of the expression.

Q: Find r'(t), r"(t), r'(t) •r"(t), and r'(t) x r'"(t). r(t) %=D 흑래- 26j + 하하k (a) r'(t) (b) r"(t) (c)…

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Q: Let 7 (t) = Find 7'(t) F'(t) -

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Q: 7.) L13x + 1|dx

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

A:

Q: ction f has the following graph: -1 4. of the following is an infinite limit? m f(r) +0+ f(x) m f(z)…

A: Topic:- limit calculus

Q: Given x – 3 x 3 - What is lim g(x) ? O 1 O -6 O –1

A:

Q: function f has the following graph: 4- 3 2 1. -1 6 7. 8 -1 -2 Vhich of the following is true? O The…

A: Given query is to find the correct statement for the function.

Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: Find div F and curl F if F(x, y, z) = 13y°z³i – 9x*z³j – 4ry°k. div F= curl F=

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = – 2tj %3D

A: 1st derivative, 2nd derivative, dot product and cross product are evaluated.

Q: Solve the differential equation Integrating Factor by Linear Equation: y' = 1 – 2ycot2x

A: We can solve this as follows:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 3…

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Q: Find the critical points of the parametric equations x = 5 – Int y = t+ Int

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Q: Daluate the Vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: the line y =4(USE DISK AND SHELL METHOD) 6.) Find the volume of the solid generated by revolving by…

A: Since the region given in question 5 is not bounded. I answer question 6 for you. Please resubmit…

Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

A: This question is related to differential equations, we will solve it using given using given…

Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

A:

Q: d,x+7 3. dx 2x-3

A: To find: ddxx+72x-3

Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

A:

Q: Find V · (V × F), if F(x, y, z) = 2e"²i+ 2xe"j – 9ev²k. V· (V × F) =

A: Given F(x,y,z)=2exzi→+2xeyj→-9eyzk→ To find, ∇.(∇×F)

Q: 6. lim (sinx)* X0+

A:

Q: Obtain the limits of the following functions: (2sinx-sin2x 1. lim x-sinx

A: To evaluate the limit of the function.

Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: Area

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

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Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 6tj – 6ik) dt

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Q: nd the general solution of the following: 2. (D3 – 4D² + 4D)y = 0 3. (4D2 – 6D + 1)y = 0 4. (25D2 –…

A: Topic:- differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: Find the Laplace Transform of the given function using the definition of Laplace Transform a. f(t) =…

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

Q: Find curl (6z i + 7x j+ 9y k). curl(6z i + 7x j + 9y k) = ( i )i + ( i )j + ( )k

A: Explanation of the answer is as follows

Q: (y – cos?x)dx + cosxdy = 0 %3D

A:

Q: Solve for k such that 1 | k(x² – 2x + 1)dx = 5

A: Given problem:- ∫ k(x2 -2x+1) dx =5  Solve for k

Q: 6. lim (sinx)*

A: