Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k (Simplify your answ

Q: 10. Find the limit using any technique. The limit of f(x) = 2x² - 3 as x approaches -3. 15 21 limit…

A: To find limit of f(x)

Q: 2 (0) IF F(x)= x 'e', Find f'(x) and F (1)

A: Finding the derivative of the function.

Q: Find the volume of the solid generated by the revolving Shaded about region the 7-axis 1 0.5 X =…

A:

Q: Find the largest triangle that can be inscribed in the ellipse (x2/a2)+(y2/b2)=1 using Lagrange…

A: answer is in next step

Q: Find the gradient of the function f(x,y)=5y-x at the point (8,9). Then sketch the gradient and the…

A: See this solution in below

Q: How many combinations can be made from ♣, ♠, ♦, and ♥ if taken a) four at a time? b) three at a…

A: solution:-♣, ♠, ♦, and ♥  are four different itemswe know that  combination is the selection of…

Q: 3 (b) / 2³ x³ cos(x¹ + 2) dx

A:

Q: (x-1) dy + (y-2) dx = 0

A: To solve the given differential equation

Q: Find a formula a, for the n-th term of the following sequence. Assume the series begins at n = 1. 1…

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

Q: For each given functions, find the slope of the tangent at a given point using first principle…

A: We have to find the equation of tangent.

Q: At 12:00 noon, there were 225 bacteria present. By 4:00 pm, there were 427 bacteria. If the bacteria…

A:

Q: Find the area under of equation x +y = 3, From x = 1 to x = 3.

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Q: 1- Use the shell method to find the volume of the solids generated by revolving the shaded region…

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A:

Q: 1. Evaluate the given integral Q. J[(y - 2x) dA, R where is the region bounded by x = 0, y = x, x =…

A:

Q: Choose one(1) from the following question to be answer. The graph of each rule must reflect on your…

A: The Trapezoidal Rule: The Trapezoidal Rule divides the whole area into smaller trapezoids rather…

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

A:

Q: air resistance can be ignored, how high does it go?

A: Given query is to find the height of the ball.

Q: 1. Evaluate the given integral Q. = [] [²³² Q L L (x - y) dx dy

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Q: Evaluate x³ dx (x4-5)4

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Q: Find the radius of convergence for the series 3 n³ xn 3n OR=3 O O OR= 8 n=1 R = R= - الله R = 1 8

A:

Q: 1. Evaluate the given integral Q. a = f £²² L [²(x - y) Q dx dy 2. Sketch the region of integration…

A:

Q: 3 Let f(x)=x* — x³. Determine the intervals where the function is - increasing/decreasing and…

A:

Q: The population of a city is 323,000. The population declines by 3.8% every year, what will the…

A: topic- exponential function

Q: 4. Evaluate the following limits. a. lim X→→→+** 2x 3x² b. lim c. lim -3/x X In5 x x²

A: This is a problem related to limit calculation. Based on the general formula and concepts we will…

Q: 14. A small, closed water tank is in the shape of a cuboid with a square base. The total surface…

A: Given :Total surface area of cuboid = 1500

Q: 1. Graph the function below Using Calculus, find the intervals where the function increases and…

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Q: (c) 1 e¹/x x² dx

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (2,4)…

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Q: Use the series to evaluate the limit tan-¹ y - siny lim y→0 y³ cosy

A: Expand series and solve

Q: 1 Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

A:

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(2,0,2) on the…

A:

Q: Evaluate the integral Sea X 6x³-1dx

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

Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

Q: The doubling time of an investment with continuous compound interest is 12.5 years. If the…

A:

Q: Find a formula bn for the n-th term of the following sequence. Assume the series begins at n = 1.…

A:

Q: Find the Taylor series for about f(x) = x³ + x² + x + 1 a = 1

A: As we know the Taylor series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where center at x=a.…

Q: e²x-2x-1 x² f(x) = a) lim f(x) x⇒0+

A: Use limit concept

Q: 8.1 PLEASE TYPEWRITTEN FOR UPVOTE. SHOW YOUR COMPLETE SOLUTION.

A: To find out the family of curves whose slope is given.

Q: A patient is administered a dose of 50 mg of a drug. If she is hooked to an IV that injects an…

A:

Q: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

A: A lighthouse L is located on a small island 2 km from the nearest point A on a long straight…

Q: Physical Applications of First-Order Differential Equations A body at a temperature of 50° F is…

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Q: 4. Find f'(x) if f(x)= In (2x) + cos (6x)

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Q: (4) Σ=o (−1)n+7 n2+3 1/1

A:

Q: 6+ З +2 (2x+1)= 8

A: 6x3 + 2(2x+1) = 8 2x + 4x + 2 = 86x + 2 = 86x = 8 - 26x = 6x = 66 = 1

Q: 7x Find the linearization L(x,y) of the function f(x,y) = e cos (9y) at the points (0,0) and 0, ¹2…

A:

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e6xy = sin…

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Q: Use the shell Method to Find the Volume of the bounded by Solid generated by by revolving the region…

A:

Q: Find the equation of the line tangent to 2exy = x + y at the point (2, 0) Write the equation in…

A: Given query is to find the equation of the tangent at given point.

Q: (-2, 39) 4 10 10 20 10 10 -20 30 40 1 (14) (27) 3 B. Locate and classify the critical point of y =…

A: The equation of the curve is given by , y=23x3-2x2-6x+2Now, We will apply the second derivative test…