Let f(x, y, z) = ey-z² X Find gradf(1, 1, -1) and G(x, y, z) = fyy- faz. УУ

Q: Question Given h(x) = tan(-x² + x), find h'(x). Sorry, that's incorrect. Try again? h'(x) = (2x -…

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Q: Consider the following function. g(x) = (x - 2)²-9 Step 3 of 4: Find two points on the graph of the…

A: Consider the function

Q: Evaluate the integral by making an appropriate change of variables. JJ₂² 7 cos(3 (y + x)) dA where R…

A: The given integral  where R is the trapezoidal region with vertices

Q: Simplify the following. Always enter your answer in the most simplified form. (a) 2√5 +3√7+8√5-5√/7=…

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Q: JO 1/8 ន √1 16x2 dx

A: By change of variables to evaluate the following definite integrals.

Q: Express your answer as a polynomial in standard form. f(x) = 2x² 5x – 12 - g(x) -2x + 2 = Find:…

A: f(x)=2x2-5x-12g(x)=-2x+2

Q: Problem #8: Use Divergence theorem to find the outward flux of = (3x², e¹², cos³ (1² + x)) of the…

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Q: Determine Ax and the midpoints of the subintervals formed by partitioning the given interval into n…

A: Determine Δx and the midpoints of the subintervals1≤x≤15;n=5

Q: 256x The volume of a sphere is increasing at a rate of 8 cm³/sec. Find the rate of change of its…

A: The rate at which the volume of a sphere is changing, To determine: The rate of change of the…

Q: Compute the curl of the vector field F = -2z7+5yj - 8x k. curl =

A: To find the curl of the vector field .

Q: 9. Suppose 0 < a <b, and Find the value of få f(x²)dx. A. 4 B. 2 C. 1 D. -5 [F(x²)dx=6₁ ["f(x²)dx =…

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Q: Evaluate the following 2 j (x² + 3x-10) dx -5 √(x²+3x-10 +3x-10) dx = -5 (Type an exact answer. Use…

A: The given integral is .The aim is to find the value of the integral.Formula used:

Q: Question Given f (x) below, find f'(x). Do not include "f'(x) =" in your answer. Provide your answer…

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Q: se the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique lution in…

A: 1) x47+8x-2=0, [0,1]2) -x100+6x+2=0, [-1,0]

Q: T (BC Topic) The length of the curve from X = 0 and.x= is given by 4 $² 1 + sec¹x dx. If the curve…

A: The length of the curve from x=0 and x=π4 is given by ∫0π41+sec4⁡xdxThe length of the curve from x=a…

Q: Evaluate I = (sin x + 2y) dx + (8x + y) dy for the nonclosed path ABCD in the figure. y C B A=…

A: Here  we have to find the integral along closed path.

Q: Problem #4: Consider SS (V x F) ndS S where F = 14ex²+y² i + 1le=³j + ln(z+2)x-cosy k and S is the…

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Q: If the birth rate of a population is b(t) = 2300e0.022t people per year and the death rate is…

A: The given data is:To find the area between these curves for

Q: lim f(x)=-5, lim g(x)=3, and lim h(x) = 3. Given x→a x→a xa the limit does not exist, explain why.…

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Q: Use Newton's method to find the positive fourth root of 5 by solving the equation x4-5=0. Start with…

A: .

Q: 1) Find 1 x² +4x+13 dx.

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Q: For Evaluate the following expression. Select the correct answer below: ={ f(x) = 4-x-x² 2x1 lim…

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Q: g(t) = t³+ t².

A: g(t)=t3+t2

Q: Consider the problem min x2 + 2x2 such that r₁ + 2x₂ = 3 #1.22 The bordered Hessian for this problem…

A: The problem is given as,such that

Q: ate and classify all (by classifying the extrema, we mean listing whether locate any stationary…

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Q: Find the area of the region between the curves y = x(1-x) and y = 4 from x=0 to x = 1.

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Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: Given,

Q: The linear density of a rod 8m long is 12/(sqrt X+1)kg/m, where X is measured in meters from one end…

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Q: Is the series ∑(1/(n + (1/n))), from n = 1 to infinity, comparable to the series ∑(1/(2n)), and can…

A: Solution is following in explanation step.

Q: Consider the following function. 1 (x-4)² Step 1 of 2: Determine the more basic function that has…

A: The given function is,

Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

A: We have given a function that models the height in feet above the surface of the water, h(t)=-16…

Q: Determine if the following function is continuous and differentiable at x = 0. ex - sin x f(x) = {…

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Q: Find inflection point(s) for f(x), if any. f(x) = 27x - x³ A. f(x) has an inflection point at x = -3…

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Q: 2 2 Find the area of the region between the curves y = 4x² - 4 and y=-3x +3 from x= -1 to x= 1.

A: The required area is the shaded region in the graph

Q: Start with the graph of the appropriate basic exponential function f and use transformations to…

A: The given function is

Q: Suppose that SpaceX launches a rocket at t = 0 seconds and that its height, in meters above…

A: Given the height of rocket is

Q: Find the derivative of the function. s= sin O A. О в. Злт 2 32 Зл 2 COS Зл OD. cos COS 0 с. COS 2…

A: Given data

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A: The objective of this question is to understand the graph of the function f(x) = 5 + 2e^(-0.1x) and…

Q: Given the following piecewise function, evaluate lim f(x). X-6 Select the correct answer below: -68…

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Q: Given the sequence an n>1 = n²-1 n+3 ' (a) List the first 5 terms of this sequence. Give exact…

A: The given sequence .The aim is to find the following values,(a) First five terms.(b) The value of…

Q: Suppose your newspaper is trying to decide between two competing desktop publishing software…

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Q: 3. g(x) x² +5

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Q: -10-9-8- -1⁰+ Given the graph of f(x) shown above, evaluate lim f(x). Select the correct answer…

A: The condition of the existence of limit at

Q: Consider moving a particle along a path given by r(t) = (e³¹, e¹, e³¹) with 0 ≤ t ≤ 1 subject to a…

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WO FOR BETTER…

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Q: Write the integral as the sum of the integral of an odd function and the integral of an even…

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Q: 0 1 2x (4 – x²) dx

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: Use complex number operations to determine the solution to the expression below. The final solution…

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Q: Find the area of the shaded region. square units 2 + 1 -1 -²4 2 +3 y=x-2 3 4 y=√x

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