Find a unit normal vector to the surface at the given point. [Hint: normalize the gradient vector VF(x, y, z).] Point (4, 1, 4) Surface x² + y² + z² = 33

Q: 2 Solve the following ODES by 1.2 • ý -2y +y = e sinx Inverse Operator method X X Anse y=cie +…

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Q: ƒx(2x−1) dx 2 √x³√x²+4 dx

A: for (1),     ∫ x2x-17dx=∫ 128x8-448x7+672x6-560x5+280x4-84x3+14x2-xdx=∫ 128x8dx-∫ 448x7dx+∫…

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Q: -6-5-4-3-2- 9 10

A: We will solve.

Q: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 2 x-intercepts…

A: We need to write an equation for a rational function with : Vertical asymptotes at x=-4 and x=2…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y² + z² (8,…

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Q: нх У - 169 = 19.2 ё + воё, усо) =ўс) 4Х 4X -4Х Ans: y=2.2 +e+24xe X - Че

A: Solution of given question is written in below steps.

Q: 1. Let r(0) = 2sin(0) + cos(Ⓒ) be the polar definition of a planar curve. Find, in standard x-y…

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Q: 9. Consider the function y = 22 with derivatives 2(6-2) dr² Find any horizontal asymptotes of the…

A: Concave Up , if the second derivative is positive . Concave down , if the second derivative is…

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Q: Use vectors to find the fourth vertex of a parallelogram, three of whose vertices are (0, 0), (1,…

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Q: What is the gradient of f(x, y, z) = x³₂² + y³z +125z - 1 at P(5,5,-1) ? 75i + 75k -75i - 75k 75i -…

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Q: What is 6x² dx?

A: We will solve it

Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t²k, u(t) = 4ti + t²j…

A: This question is based on dot product of two vector. (a i + b j).(c i + d j) = ac + bd

Q: Find all values of x and y such that Px(x,y) = 0 and P Py(x,y)=0 simultaneously. P(x,y) = 5x² -…

A: Topic = Algebra

Q: Find the domain of the function. (Enter your answer using interval notation.) F(x)=√x + √7-x

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Q: Find a formula for the inverse of the function. \\ f(x) = f-¹(x) = 1+e 1-e

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Q: Four partners are dividing a piece of land worth $159,200 among themselves using the lone-divider…

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Q: We have found the following Wronskians. W = −e-³x; W₁ = −e-²x (4 + ex)-¹; W₂ = e¯x(4+ e*)-¹ Р We…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: e) Find the linear approximation of the function f(x, y, z) = x³y² + z² at the point (2, 3, 4) and…

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Q: (2x +3y) dx + (y +2) dy = 0

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Q: Find the Laplace Transform of f(t) = sin2tcost A B 2 54 +55² +4 2 Ⓒ 4 E s² +3 s+10s² +9. ( 5++55²+4)…

A: Given problem:- Find the Laplace Transform of f(t) = sin2tcost

Q: 64 Use the first derivative test to answer the following: the function f(x) = 49x + I and a local…

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

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Q: (e) Find the linear approximation of the function f(x, y, z) = x³ √√y² + z² at the point (2, 3, 4)…

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Q: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

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Q: A math teacher won a lottery that pays $1,000 per month for the next 20 years. But, he prefers to…

A: To find out the amount that the teacher will accept now.

Q: Consider the following second-order differential equation. 2y" + y = 0 Find all the roots of the…

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Q: 5. 6. Sexcos2x dx |— S- dx 3 (x + 2)² − (x+2) ² -

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Q: 1 if x > 0 x²-1 if x ≤0 g(x)=x-1

A: Given the function, gx=1x-1if x>0x2-1if x≤0

Q: Find all solutions of the equation 4 cos(3θ + π/4)+2=0 in the interval [0,2π].

A: Solution of given question is written in below steps.

Q: 1. DIFFERENTIAL EQUATION (2y³ + 4) dx = (6-2xy²) dy

A: Note :- These are multuple questions and according to our comapny guideline we can do maximum 1…

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Q: ∞ Determine whether the series (-1)"- n gent, or divergent. n=1 is absolutely convergent,…

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Q: 1. Sketch the graph of r=1-cos in polar coordinates. [3 marks]

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Q: Consider the following function. f(x) = 4x² - 7x² Determine whether the function is even, odd, or…

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Q: Write an equation for the function graphed below. The y intercept is at (0,-0.2) -7 -6 -5 -4 -p 2 y…

A: To find the equation for the function.

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Q: Given f(x) = x² + 7x + 6, find the following. (a) f(0) (b) f(1) (c) f(-1) (d) f(-3) (e) f(a) (f) f(x…

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Q: Determine whether or not F is a conservative vector field. F(x, y) = (my + ²)i + (mx + 7);

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Q: Write an equation for the function graphed below -7 -6 -5 -4 -3 -2 5+ 4- 3- 2 1 -2- -3 -4- -5+ 1 2 3…

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Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

A: Given: the volume of swimming pool = 10000 gal that contains 0.03% chlorine. at t=0  ,0.002%…

Q: 23. Express each of the following as a logarithm. Use a calculator to evaluate your answer correct…

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Q: 4. Condense the log to a single log expression. a. 2 log y - 3 log x - 2 log 10 b. Ina+3 ln y

A: See this solution in below

Q: Find the area bounded by y = x(x-1)^2, y = - 2 and the line x = A 10/3 = 2 B 5/3 C No of the options…

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