Example 5.4.3.1 1. Find the maximum rate of change of f at the given point and the direction in which it occurs. f(s, t) = tet, (0, 2)

Q: 6. f Vesx + etx dx

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Q: Evaluate the integral: ſo (x³ – 5æ + 7)dx. Select one: O None. 19

A: Given :∫01(x3-5x+7)dx

Q: Check if the following is true or false: (x² + 3)dx = 18 %3D

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Q: 1.5 (0,7, 0.2y f0.7,0.2) O5 ー15 - O.5 0.5 1.5 -0.57 (-1,2,-1) -15 -2

A: The f' is undefined where the graph of f has shard edges that is at x=-0.7,0,0.7,1 f(x) has sharp ed...

Q: t T F(x) = | In(4 - t) cos dt 9. 3 Find F(3) b. a. F'(3) F"(3). You must show your work. C.

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Q: 3. tan(xy) + xy -0

A: Question number 3,Given,           tanxy+xy=0To find : The second derivative, y'' of the given funct...

Q: dx

A: Topic = Integration

Q: つC 人ny dy de //ヶ。 1 = 1. 1.

A: solution:-∫12∫1xln yxydy dx=∫12∫1xln yxydy dx=∫12ln y22x1x dx=∫12ln x22x-ln 122x dx=∫12ln x22x dx=ln...

Q: 1- cos A + sin A - then 2 sin A is equal to If y = 1+ cos A + sin A 1+ sin A 1 y y Option 1 Option 2...

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Q: | 120 sec(a + 10) tan(a + 10) da .3

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Q: 6. Evaluate the improper integral 3dx. Use limits as needed. Give exact 2 answer. . 3

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Q: Find two unit vectors in 2-space that make an angle of 45° with 7i + 4j.

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Q: 1) Which set of values for x should be tested to determine the possible zeros of the function f (x) ...

A: We need to find possible x values that needs to be checked where function is zero.   NOTE - As per B...

Q: 2sim x-1 -y = COST+2

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Q: Determine whether the given series is convergent or divergent. +oo 5n + sin? Σ - | sin n| а. 3" n=1 ...

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Q: Find the diameter of the of the circle with center at (-5, 3) and tangent to the line 8 – 2x = 2. O ...

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Q: Let the region R be the area enclosed by the function ƒ (x) = /x +2, the horizontal line y = 2 and t...

A: The given problem is solved below in detail.

Q: dx - = In[F(x)]+C•What is f(/3) For if C = 0? (x+x³) (x Tan-!x+ 1)

A: A detailed solution is given below

Q: 2. A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in...

A: Given that a rocket is launched in the air. Its height , in meters above sea level as a function of ...

Q: If 5 tan 0 – 4 = 0, then the value of 5 sin 0 – 4 cos 0 is 5 sin 0 + 4 cos 0 - 3 Option 1 Option 2 1...

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Q: Solve the following triangle. B= 70°, C= 30°, b=7 (Simplify your answer) (Type an integer or decimal...

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Q: Evaluate the improper integral or state that it is divergent. dx (x-6Xx-5) O In 6 O In 7 In 2

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Q: mydx = nxdy Ans. x" = cy"

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Q: Verify that the series Σ n +1 n=1 satisfies the conditions of the Integral Test, then use the Integr...

A: The given series ∑n=1∞nn4+1

Q: A small town is known to grow its population at a rate proportional to the population at any time. A...

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Q: I Find the second derivatively") of the following functions and simplity the final results. 1. y=x-x...

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Q: The table below gives selected values for the differentiable and decreasing function f and its deriv...

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Q: The expression below is an evaluation of which integral? * 6x + 3 ln|æ – 2| – 18 ln|æ + 4| +c 2x2 – ...

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Q: ·sec-x)" sec'x 23. What should be the value of A for -dx to be integrable using the formula | u" du?...

A: the integration of the integral is (2-sec2x) eln(pi/e)sec3x/Sec(3A-x).

Q: Exercise 7. Let (1 3 0 A = 30 1 0 1 1 1. Find the eigenvalues and associated eigenvectors of A. 2. C...

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Q: The function A Age0.19t models the amount an individual owes a credit company t years after some ini...

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Q: xtra questions: Find the Derivative of 8 1. y = 10 vx ++ x2 2. y = ta n(si n x) 3. у %3D cot?3x

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Q: xcos³x² The S dx is 1-sin x? sin?x² + C {c}sin x² +sin²x² + C {D}sin x? –sin²x² + C { A} sin x² 2 4 ...

A: This question can be solved using integration by substitution.

Q: F (x. y) =- 3x2+3y2-18y+15 4- /2x+4y+4 a) Find domain b) Draw sign Diagram

A: Given Functionfx,y=3x2+3y2-18y+154-2x+4y+4We will find the domain and Draw sign diagram

Q: Consider the function f(r) - on the interval 2, 6. Find the average or mean slope of the function on...

A: f(x)=1xInterval [2, 6]f(2)=12f(6)=16The mean slope=f(6)-f(2)6-2Mean slope = 16-124Mean slope = -44(1...

Q: 5. Sketch the graph of the logarithmic function f(x) = log, x, State the domain, range and asymptote...

A: This question is based on Logarithmic graph and it's properties.

Q: Find the area bounded by the x- axis and the graph of the function f (x) = 4x² + 8x +1,0 <x 3. (4 II...

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Q: dr = b(cos Odr +r sin Ode) Ans. r = c(1-bcos 0)

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Q: Let P(t) = (x,y) be the terminal point on the unit circle that corresponds to the real number t. Fin...

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Q: 2. Find the slope of the tangent 2 line to the curve f (x) = - = -1 at x

A: topic - slope of tangent line to curve

Q: Find all critical points of the function f(x) = x-15 – x-16. (Use symbolic notation and fractions wh...

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Q: Use the Integral Test to determine if the series 1 Σ (n +2)°/¾ n=1 converges or diverges.

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Q: 5. y = xArctanx - In VI+x

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Q: Evaluate the integral. Answer should be expressed as a decimal value (5 decimal places, example 0.01...

A: Put y =5secthetha and solve it. 

Q: 2. Find the slope of the tangent line to the curve f (x) = -1 2 at x

A: Given: f(x)=2x

Q: CHAIN RULE DERIVATIVES Directions: Differentiate the given fnctions 7) gx) = 13lbc" (5bt 4c t 9)s

A: Given function g(x) = 13bc3(5b+4c+9)5 Find:- Find differentiation with respect to 'x'

Q: Let {an}=1 be a convergent sequence such that a1 = V5 and an+1 V5 an. Compute lim an.

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Q: Question 1 2dy Evaluate the integral Зу — 4

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Q: +00 e-*dx

A: Topic = Integration

Q: 15. (ez + e-z)2 dx.

A: Given: I=∫01ex+e-x2dx As we know from the hyperbolic trigonometric identities; 1). sinhx=ex-e-x2 2)....