Question 6 Consider the function below: sin(x²+y) { (x, y) # (0,0) (x, y) = (0,0) f(æ, y) y-x Find the value of the derivative fr at the origin (0, 0).

Q: 15. a, = (-1)" 3n-

A: since we are given with multiple number of questions and our guideline is solve the first question o...

Q: (2x -y+2)dy + (x-2y +4)dx =D0

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Q: Given the function f(x) = x* – 24x², determine all intervals on which f is both decreasing and conca...

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Q: Express the composition W (x) in the form f • g • h. W (x) = - 7 х — 7

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Q: If z = eax+by az then a az is ay

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect ...

Q: Determine the maximum and minimum points of the given functions below. f(x) = 3x4 – 16x3 + 24x2

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Q: In November 2021, the stock price for an Apple Inc has increased from $131 to $148 per share and Ama...

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Q: Let u = (-2, -2), v = (-5, O (0, 2) (-1, -3) O (-7, -5) O (-3, -1)

A: Vector, a quantity that has both direction and magnitude.

Q: Calculate the derivative of the following function. y=f(g(6x*)), where f and g are differentiable fo...

A: We have to find out

Q: Consider the given function and the given interval. f(x) = (x - 7)2, [6, 9] (a) Find the average val...

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Q: Solve the following equation for x. log(4x+170) = 2

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Q: 25. Evaluate the following definite integrals. e) L, 3wv4 – w2 dw

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 8 ka > 2sin 2 ...

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Q: Given the following table, give the best estimate for f'(9) – f(9) Co 3 6. 9. 12 15 f(x) 30 43 53 61...

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Q: Expand (2+V-9) А. 46+9i В. 46-9i С. -46-9i C. D. -46+9i

A: Option (D) correct. For detail go through the solution

Q: sinº – cos? –dx 2 2

A: We have to find the integral of the above function.

Q: The function f is shown below. What is the value of | f(x) dæ? Writey your answer in simplest form. ...

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Q: (2) Compute the following integrals. *T/4 (a) ) sin (4r) cos (4xr) dar. (b) / cos(kx)e l dx, Hint: c...

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Q: Determine (in ordered pair) the point of intersection of the lines 2x – 5y = 10 and 3x + 2y = 6.

A: Intersection of two lines- Intersection point will satisfy the equation of both lines .

Q: Find the volume V of the described solid S. The base of S is a circular disk with radius 4r. Paralle...

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Q: 14. Evaluate the following limits. a) lim (x² + 2x – 3) X-0 b) lim (x3 – 2x² + 3x + 4) X-

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Q: 3. Determine whether or not each equation is a function. Justify your answers. a) y =- 2x + 5 b) x? ...

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Q: 23. Find the point c that satisfies the mean value theorem for integrals on the interval [1,4] for f...

A: The given function is: f(X)=2x2-7x, [1,4]

Q: 11. Use the definition of the limit of a function to prove that lim g(x) =- 6 if %3D (16x²-9 4x +3 3...

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Q: Imaginary and Simplify: 1) (4 + 2i) + (-3 – 5i) 2) (-3 + 4i) – (5 + 2i) 3) (-8- 7i) – (5 – 4i) 4) (3...

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Q: x2 dx J V4x – x²

A: Given:       ∫x24x-x2dx    =∫x24-x-22dx  substitute u=x-2→dudx=1→dx=du                    use x2=u+2...

Q: O Use a linear approxi mation (differential) to estimate 3999

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Q: 2.2) Solve and explain the steps involved. (2+7a)e dr

A: In this question we have to solve Integration.

Q: 1000 The logistic growth model P(t)= represents the population (in grams) of a bacterium after t hou...

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Q: 5**+2x (2x3 +1)dx *(2x3+1)dx

A: I have stated the used formulas in the solution.

Q: Question 19 * 19. Differentiate f (x) = 3 ln (2x –1)´ with respect to x . 12 S"(x)=- 2x-1 A S'(x)=: ...

A: Given :f(x)=3ln(2x-1)2

Q: Use the Chain Rule to find dw for w = dt xe7,x = t2,y =1- t,z = 1+ 2t.

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Q: For what values of x is y = 150x - 2x3 an increasing function?

A: For the function to be increasing the derivative of the function should be greater than 0

Q: 8. A company is increasing production of oven mitts at the rate of 4 per day. All oven mitts that ar...

A: Revenue function , R (x) = x P(x) Where P is the demand function  and x is the  price per unit.

Q: A mountain climber wants to climb up a mountain that is 1 000 meters high. In the first hour, he cli...

A: A mountain climber wants to climb up a mountain that is 1 000 meters high. In the first hour, he cli...

Q: Write the first five terms of the sequence: 13 ln n n n=1 Determine whether the sequence converges, ...

A: Given

Q: 10 10 Evaluate 5x dx using the trapezoidal rule and Simpson's rule. Determine The value of 5x dx is ...

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Q: 27. Use the disk method to find the volume of the solid generated by the region bounded by the line ...

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Q: 13. The cost of a data plan is $45 a month, plus $0.40 per gigabyte of data downloaded. Let f(x) be ...

A: Given: $45=fixed Cost of data plan$0.40=variable cost of data per gigabyte or gb$2=fixed part of con...

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places acc...

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Q: Find dy by implicit differentiation. dx x³ + y3 + 2y - 8 = 0 dy dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Identify all singular points and points of discontinuity of the given function. HINT [See Example 3....

A: Since function is not differentiable at x=5  So, singular point is x=5  But function is continuous e...

Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then, ...

A: Solve for average temperature after 40 min. 

Q: п (п Let d e R. For the arithmetic series (n-1) d, verify that sn = n=1 Also, show that an arithmeti...

A: We will check the divergence of the arithmetic series. 

Q: DIFFERENTIAL EQUATION Find the differential Equation of the family of the curves described. Draw at ...

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Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. f(x.y) =x - 5xy + 6y ...

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Q: Use the trapezoidal rule with n = 5 to approximate cos(a) - d.x Keep at least 2 decimal places accur...

A: ∫15cos(x)xdx ; n=5

Q: 14x - 39 * The partial fraction decomposition of can be written in the form of 12x2 - 13x - 14 f(i) ...

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Q: nd the derivative of the function. (6 – x)5/4' x4/5 y = In

A: We will find the derivative. 

Q: Solve ( V42 dx then evaluate the answer at x=-39 and C=34

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