23. sin 20 cos 20 dên

Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find «(t). 13 r(t) = t'i+ t®j 30 t3 K(t) V4 + 25…

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Q: Determine the vector field of F. F(x, y) = yl – x) 1.

A: Vector field

Q: Evaluate the integral of (3x2 + 9y2) dx dy if the interior limits has an upper limit of y and a…

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Q: Find a Taylor Series for the function about x = 0. F(x) = In(3 + 4x) %3D

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5…

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Q: Find curl (4zi+ 5xj+8yk). curl(4zi+ 5xj+ 8y k) = ( i )i + ( i )j+( i %3D

A: As we know that; The expression for the curl of the vector point function F→=F1i+F2j+F3k is; curl…

Q: d. | x In(x + 2) dx

A: This question is related to definite integration, we will solve it using given information.

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||³ r(t) = 3 cos(2t)i+ 3 sin(2t)j + tk…

A: The given formula is: κt=r't×r''tr't3 And rt=3cos2ti+3sin2tj+tk   As we know that; The Chain rule;…

Q: Find div F and curl F if F(r, y, z) = 2e""i – 9 cos yj+ 4 sin? z k. div F= curl F

A:

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: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D %3D a. Write the unit vector for s- b.…

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Q: Solve for all values of x. 1, 12x+9 6-322+9 36 Answer: Submit Answ

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Q: ,2 dy 2х dy + 2 dx -9 —D 12х — е dx?

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Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

A:

Q: A lighthouse is on an island 250 meters off shore. The lighthouse beam makes a full turn every 7…

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Q: Find curl (2z i + 3x j + 5y k). curl (2z i + 3x j + 5y k) (i )i + ( i j+ ( i )k

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Q: 26) In Problem 26 and 27, given f(x)dx= - 1 J g(x)dx= 2 and S f(x)dx= 3 a a d. Find f" f(x)dx + S*…

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Q: Hi, I believe the function was not entered correctly in the transcription. It should be x^2-16/x-2.…

A: Apologies for the inconvenience. First two steps were correct in the original solution. Step 3 was…

Q: if x 1. z +1 Given f(x) = 2x 1 Then, lim f(x)%= 2+1+ O does not exist O 2 0 1

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Q: tanx dx I+x?

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Q: y" + 2y' + 5y = 4e¬t cos 2t, y(0) = 1, y'(0) = 0 %3|

A:

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: Find div F and curl F if F(x, y, z) = 3e™Y i– 3 cos yj+ 10 div F=

A: Given: 3exyi-3cosyj+10sin2zk

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

A:

Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x2 – 9…

A: Given

Q: INSTRUCTION/S: Evaluate each limit by two methods. TOPIC: INDETERMINATE FORMS FIRST METHOD (Partial…

A:

Q: Using appropriate substitution | sec*x dx is equal to In|secx + tan x| -1 + C 2cos?x + sec x tan x +…

A:

Q: 2. The sum of a two-digit number is 13. When 27 is added to the original number, the result is the…

A: To find out the original number.

Q: Solve the differential equation Bernoulli Equations: dy + бу — Зху3 dx 4 3xys

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

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

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

A:

Q: Definite Integral. 2.) S x²(2x³ + 1)*dx 4.) x?e*dx 6.) f- xp:

A: To integrate.

Q: Exercises Distinct Real Roots of Auxiliary Equation Find the general solution 5. (D² – 1)y = 0

A:

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2…

A: To write down that it satisfies the mean value theorem or not.

Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 25 sin…

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Q: 1. Using L'Hospital's rule, evaluate lim(1 – x²).

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Q: Find the area, A, of the region enclosed by the cardioid r = 8+8 cos 0.

A: Given   area can be given as below :

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

A: we use the basic formula ∫xn dx =xn+1n+1+C    ; n≠-1

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = eti+ etj K(t) :

A: Given r(t)=e5t i + e-t j

Q: I. Evaluate the following Definite Integral. 1.) Lº 6x³+4x²-8x 2.) x²(2x³ + 1) dx dx 2x 3.) sin…

A: Given

Q: Find the volume of the solid generated when the region enclosed by the given curves is revolved…

A: Plotting given curves on the graph

Q: Describe the graph of the equation. r= (5 - 31) i - 10:j O tis a line in 2-space that goes through…

A: This is a problem related to vector. Based on the general formula and concepts we will answer the…

Q: Determine the nature of convergence of the following improper integrals +00 1 X A = dx 1+x4 x 2 dx…

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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: ±∞±∞ ;…