1. Given z = 16 – x²- (a) Find the domain and the range of the function. (b) Sketch the level curves of the function for z = 0, z = 1, 2 = 2, and the surface of the function.

Q: 1 2 #5) A) Find the length of a curve y Inx for 3 < x < 7. 4

A: L= integration of sqrt of 1+ (dy/dx)2 dx from a to b

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: Find the exact length of the curve. y = 3 + 2x^(3/2), 0 less than x less than 1

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Q: Sketch in the two level curves of: f (x, y) = y+ x² = k _for k = 1, 2.

A: Solution is written in below steps.

Q: What is the slope of the tangent line that touches the graph of In y +es-1 = 3y – 4z at the point…

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Q: Find the slopes of the tangent lines to the graph of f(x) = 2e² at the points (0, 2) and (1, 2e).

A: See the attached file to know how to find thesthe of a tangent at the given points.

Q: FIND THE LENGTH OF THE CURVE y = In sec X from X = 0 to X = - 4

A: Given curve is y= lnsecx .  We have to find the length of the curve from x=0 to x=π4. Length formula…

Q: 1. Find the length of the curve y = 3 xi - () x , from x = 1 to x = 4.

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Q: If the length of the curve y = 3 x7 from the point (0, 0) to the point (xo, f(xo)) is L = 8 , then…

A: Length of curve

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

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Q: Find the sketch of the level curve flx, v)-c form and f(x.y) 100-x2-y and c- 0.

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Q: (i) Find the values of k for which y= kx + 2 is a tangent to the curve y= 4x2+ 2x + 3.

A: If y = kx +2 is tangent to the curve y=4x2+2x+3, then the point of intersection of the line and the…

Q: x = e' and y = te %3D

A:

Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: find the tangent line to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: Given the parabola x+2y2+2x-y-3=0..............i  Determine the slope of given line x-4y=2…

Q: Find the points on the graph of x^2+2x+4y^2=4+y where the tangent line is horizontal

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Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: 3. Find the length of the curve y =x* +÷x¯² from x = 1 to x = 4

A: 3 Given function isfx=y=18x4+14x-2  from x=1 to x=4now we can writen as fx=x48+14x2 on 1,4The lenght…

Q: , If the curves yı = -x² + ax +b and y2 x² + cx - 2 have the common tangent line at the point P(1,2)…

A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: 2 2 18. At how many points on the curve + yš =1 in the TY-plane does the curve have a tangent line…

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Q: The length of the curve y = from x = 0 to x 6 is

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Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

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Q: Find the length of the curve y = 1 - e^-x, 0 &lt;=x&lt;=1.

A: The given curve is

Q: Determine the value of a, given that the line ax+y+1 = 0 is tangent to the graph of y= ax-6x+1 at x…

A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: The tangent plane to the graph of the function :==3y+1=(1+y} at the point (1; 1; 3/2) contains point…

A: The given equation of the surface is z=x2y+1. Rearranging the above equation gives, w=z-x2y-1 Find…

Q: The tangent line to the graph of y = In(2x) is perpendicular to x + 4y = 1 at the point where…

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Q: Let f(6) = -3 and f'(6) = 8. Then the equation of the tangent line to the graph of y = f(1) at z = 6…

A: The standard equation of the slope-intercept form helps to find the required equation of tangent.…

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

A: We know that equation of tangent plane to the graph z=f(x,y) at point (a,b,c) is…

Q: Plot the level curves for c = -2, -1, 0, 1, 2, for the function f(x, y) = 5x + 2y2 using geogebra

A: Given : f(x,y)=5x^5 +2y^2 To find: To plot the level curves for c=-2,-1,0,1,2 for the given function…

Q: 9. Find the point on the curve y x² closest to the point (0, 1).

A: As per bartleby guidelines we only give first question answers.

Q: Find the length of the curve y = 4 1 between x 1 to x 2. %3D &x2

A: It is length of curve.

Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

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Q: Find the exact length of the curve y = (2/3)(x^2-1)^(3/2), where 1 is less than or equal to x which…

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Q: If the length of the curve y = 4 x7 from the point (0, 0) to the point (Xo, f(xo)) is L= 1 (145)*…

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Q: Find the length of the curve defined by Y=5x^3/2+9y from x=1 to x=8.

A: Given that

Q: Find the values of a and b for the curve x2 y + ay2= b if the point (1,1) is on its graph and the…

A: Find the slope of tangent line

Q: find the length of the curve on the given interval: y=1/3(x^2+2)^(3/2), [0, 1]

A:

Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

Q: Find all the points of the graph of y = (x - 2)2 at which the tangent line is perpendicular to the…

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Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: The length of the curve y from x=0 to x= 6 is

A: We need to find the length of the curve  y=23(x2+1)32 from x=0 to x=6

Q: Find

A:

Q: Two different level curves of the graph of z = f(x, ygan intersect. O True False

A: The level curve of a function f of two variables are the curves with equations f(x ,y)= k, where k…

Q: Does the graph of S0, x< 0 U(x) = 1, x2 0 have a vertical tangent line at the point (0, 1)? your…

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Q: find the under the curve y=7-t^2 and above the t-axis

A: