Choose the gradient of the function : f(x, y) = ex² Select one: O None of these ○ (6ye+²+³y², 2xer² + ³y²) O (6e²+3y² ², 2ez² + 3y²) O (2xe²²+3y² 6ye™² + 3y²) O (2e²+3y² 6ez² + ³y²) 9 " +3y²

Q: If L{f(t)}=F(s), evaluate F(2), f(t) = 1 + 2t - (1/3)t4 O 0.75 O 1.25 O 1.50 O 1.0

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Q: The ceiling of a building has a height above the floor given by z = 30 + x, and one of the walls…

A: The surface area can be given by SA=∫abf(x)ds =∫040(30+14x)ds Path is given by…

Q: What is the value of the integral Select one: O 64 O 16 O None of these O 32 4 SS 0 X 08 2xydydx?

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Q: Use the properties of infinite series to evaluate the following series. 3. 5" Σ n=0

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Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

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Q: 4. Compute the total volume of the shaded area of the figure below where the cross-sections are…

A: We need to find volume.

Q: 8) Use the functions f(x) = x² and g(x) = √2-x to find the specified function its domain: a.…

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Q: q+m (v) m Submit Question 2 1 -6 -5 -4 -3 -2 -1 -1 2 3 A 16 5 1 Find an equation for the graph…

A: General equation  m=AsecBv-c+d Now we need to find A,B,C and D

Q: 7. Let C be the portion of the circle x² + y² counterclockwise. (a) (b) Evaluate La xy dy. = 4 from…

A: Let's solve given integral.

Q: Solve the given initial-value problem. y(x) = y" - 81y = 9, y(0) = 1, y'(0) = 0

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Q: Create a table of values for the function and use the result to estimate the limit. Use a graphing…

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Q: bn = n' ебп

A: Here, the given sequence is bn where bn=nne6n

Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

Q: Consider the function f(x) = x³ + 9x² + 15x. Step 1: Find all values of x that correspond to…

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Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

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Q: Consider a projectile launched at a heighth feet above the ground and at an angle with the…

A: The parametric equation of the position of the ball is given by…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given that , Point =0,0,0 and parallel line r=3+2t , 7-6t , 5+4t find vector and parametric equation…

Q: Problem 100. Evaluate the double integral re R is the region bounded by x = 0, y = 2, and y=x. R y…

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Q: Sequences have many applications in mathematics and the sciences. In a recent paper³ the authors…

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Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: 2 4 23 4 4 f²f3x³y²dxdy = f²y³ dy fx¹dx Select one: True O False

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Q: If you evaluate the integral expression 2x+1|dx the -2 result is Blank 1 (use fraction or decimal in…

A: To find out the definite integral.

Q: 2. [ sinxcos’xdx

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Q: Which of the following are true of vertical asymptotes? Select all statements that are true.…

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Q: Find linearly independent functions that are annihilated by the given differential operator. (Give…

A: The characteristics equation is (m-3)(4m+5)=0. So,                   m-34m+5=0⇒m-3=0  or…

Q: Use the properties of infinite series to evaluate the following series. k 20*30*] Σ + 6 4 5 6 k=1

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Q: Find the average temperature in the box D = {(x,y,z): 0≤x≤ In 3, 0sysin 9, 0≤z≤ In 27) with a…

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Q: A sales representative for a company that produces blenders can sell x units of their deluxe model…

A: To marginal profit is the derivative of the profit function, which is based on the cost function and…

Q: d the length of the dashed zig-zag path in the following figure. X+ 0.75+ 0.5+ 0.25+ 00.25 0.5 0.75…

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Q: By using trigonometric substitution, evaluate the following integral IVF x √²+6x+10 dz

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Q: 2- The work can be computed as: W = fp dv. Using a combination of the trapezoidal rule, Simpson's…

A: Here we have to use trapezoidal rule , Simpson's (1/3) rule and Simpson's (3/8) rule

Q: f(x) = 5* g(x) = log5 (²²= 4) Find (fog)(x) and obtain its domain. h(x): - 6 <- x 2x-5

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Q: ition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the…

A: Please see the below picture for detailed solution.

Q: The side of a square is growing at the rate of 5 centimeters per second . Find the growth rate of…

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Q: (a) Find the length of the curve y=[^ √√√²-1dt, 1≤x≤ 16.

A: To find the length of the curve.

Q: Using the function g ( x ) = 2x³ - 6x , determine the intervals where the - function is increasing…

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Q: Find an equation or inequality that describes the following object. A sphere with center (4,1,1) and…

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Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Find the first three terms of the sequence using the explicit formula 3 × (10)(n -1). A.10, 30, 90…

A: topic - sequence and series

Q: y = 9x6 - 81x4 (Use symbolic notation and fractions where needed. Give your answers in the form of…

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Q: = √ F Evaluate F. dr. F(x, y) = 3xi + 4yj C: r(t) = ti + √4-t²j, -2 ≤ t ≤ 2

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Q: Find the cross product a x b. a ++kb-i+2j - 3k 10 Verify that it is orthogonal to both a and b. (a x…

A: Consider the vectors  a=12i+13j+110k,    b=i+2j-3k

Q: (d) Find the volume of the solids generated by revolving the region in the first quadrant bounded by…

A: We need to find volume.

Q: Solve the given differential equation by undetermined coefficients. y" - y' - 30y = e6x y(x) =

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Q: L4Q16. The first term is 4, and the explicit formula is Tn = a + 5(n - 1). Find the 7th term of the…

A: The first term is 4, and the explicit formula is Tn = a + 5(n - 1). Find the 7th term of the…

Q: 2x 4) y" + 6y' + 5y = 2eª + e²x.

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Q: -4 - Find the derivative for the function f(x) = (5x−4+ 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A: Given, f(x)=5x-4+3x+78x-3-7x+105

Q: 8-x-1² if x 2 Calculate the following limits. Enter "DNE" if the limit does not exis f(x) Let f(x)…

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Q: Find the equation of the tangent line to the function f(x) = ln(5x) at x = 8. (Use symbolic notation…

A: We have to find out the equation of tangent

Q: en differential equation by undetermined coef y = x²ex + + 3

A: