Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

Q: Solve the D.E. (x +3y )dx- 2xy dy = 0

A: Find your answer below 

Q: 2. We want to integrate a function over the region bounded by x = y2 - 1 and x = /1- y2. What should...

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Q: Find the equation of the normal line to the graph of ey tan(xy) − ln(x2 − 4y) = sin2(πx) at the po...

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Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = - 1- 2x Provide your a...

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Q: d²y Find dx2 if –10x – 6y = -6.

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Q: Integration by Parts - Indefinite Integral Let u = f(z) and v = g(x) be functions with continuous de...

A: Integration

Q: In Exercises 33-36, use upper and lower sums to approximate the area of the region using the given n...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

A: Find your answer below 

Q: The regions A, B, C, D, andE in the figure below are bounded by the graph of the function f and the ...

A: Here, ∫-40f(x) dx=∫-4-2f(x) dx+∫-20f(x) dx

Q: Consider the following tables: -2 -1 1 2 f (x) 5 -3 4 3 -2 -1 1 g (x) 5 1 3 Fill in the blanks with ...

A: Function values of f and g are given, we have to find the following.

Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at'x = =. (Enter an exac...

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Q: (a) Show that the following identity is true 1 1 2n +1 n2 (n+ 1)² n²(n + 1)² (b) Use the identity in...

A: Sum

Q: Find the total differential of the function f(2, y,) : y + z' df = dæ + dy + dz (y+2)* (y+2)* y+z dz...

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Q: Find all solutions to the equation on the interval 0, 27) : cos (a V3 - 2 * 47 3' 3 47 57 3 3 * 27 4...

A: Given query is to find the solution of the equation.

Q: Given f(x,y) = 3x sin(3xy). Find fx(3,2). Give you answer correct to two %3D decimal places. Answer:

A: Topic:- partial derivatives

Q: 2x + 200 A garden shop determines the demand function q = D(x) = during early summer for tomato plan...

A: Elasticity

Q: 2. Let C be the graph of the equation In(3y – 2e*) = sinh (Tx) – tan(y – 1) dy (a) Find dx (b) Find ...

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Q: Given f(x,y) = 3x sin(3xy). Find fxy(3,2). Give you answer correct to %3D two decimal places. Answer...

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

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Q: Trigonometric Substitutions The three basic trigonometric substitutions are in the table below. Inte...

A: topic- indefinite integral

Q: Write out the first three terms and the last term. Then use the formula for the sum of the first n t...

A: Given query is to find performed indicated operation for arithmetic sequence.

Q: . Three waka ama teams are on the uta (shore) waiting to race. These teams are imaginatively named A...

A: We are authorised to solve only one question. With 3 subparts, please repost remaining parts Equatio...

Q: General Solution of a First Order Linear Differential Equation A first order linear differential equ...

A:

Q: 28) S idx=f /2dx, 28) B)5/2.C D)글지/2.c 29) J 3.²dx=. 29) A) x3 B 3x2 + C C) 6x + C D) x3 + C 30)5sin...

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Q: 4. A concert promoter has found that if she sells tickets for S50 each, she can sall 1200 tickets, a...

A: Explanation of the answer is as follows

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is...

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Q: Can Mean – Value theorem applied for the following function - on the indicated closed int erval ? If...

A: The objective is to check that can we apply mean value theorem for the function on the indicated clo...

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

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Q: Evaluate each expression. 12. logs 216 10. log, 32 11. log, 1

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Q: Use A not d or h f(x)=6x®+3x²-7 f(x)=2x^+5x²-5 f(x)=9x³+7x>-16

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Q: 1. Find the directional derivative of f(x,y) = In(a2 + y²) at the point P(2,1) in the direction of t...

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Q: Q Find Haclaurin Sertedf then fuucboors Ć Sinx

A: Here we have to find the Maclaurin series of the given function,  a) f(x)=11-xb) f(x)=exsinx  

Q: Evaluate the integral. 4 3* dx /3

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Q: Let f be a function defined by z = f(x, y) = 3xy? – 4y. Find the actual change in z when x changes f...

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Q: Suppose 2700 cm² of material is available to make a box with a square base and open top. a) Show tha...

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Q: _t f'(x) = tª – t3 + t² + t – 1

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Q: 7t + 4 lim t→-∞ t2 + 1 – 7t

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Q: Find a value a > 0 so that the graph of the exponential function f(x) = a" contains the point (3, 1/...

A: The point lies on the curve, so the point satisfies the given function.  

Q: Use sigma notation to write the Taylor series about x = xo for the function. 9 In x; xo = 1 1 |(-1)*...

A: Take the derivative multiple times and observe the pattern then substitute in the formula for Taylor...

Q: The regions A, B, C, and D in the figure below are bounded by the graph of the function f and the x-...

A: Given query is to find the average value of the function.

Q: Consider the polynomial equation a + 2x³ + 22x? + 50x – 75 = 0 a) Use synthetic division to show tha...

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Q: Write down the first derivative of each function in the space provided. Do NOT simplify your answers...

A: Solving questions 

Q: 4.- The population of zebra in an area varies around an equilibrium level X.. The population of lion...

A: We will answer to the question 4a only as it is mentioned and demanded. 

Q: Let k(x) = (4x2)g(x)h(x). Given the following table of values, find k'(1). %3D -1 0 1 3 h(x) 1 -3 0....

A: Use the table and chain rule to differentiate the function. 

Q: lim 1-2 2x2-x-6 -1 lim -2

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

Q: The position of a car traveling along a highway is given by the function s(t) = 2t* – 2t - 3t2 + 6 w...

A:

Q: Consider the following tables: -2 -1 1 2 3 f (x) 2 5 -3 4 -101 -2 2 g (x) 5 4 1 2 Fill in the blanks...

A: topic - composite functions

Q: 23) Find the SLOPE m = at the point (2, 0). [Hint: sin 0=0 and cos 0 =1] A) 2 of a tangent line to t...

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Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=5 and x...

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Q: Given f(x) = 2/x + 5 and g(x) = 2x^2 − 5, find f(g(x)) and g(f(x)).

A: Let's find.