Problem 1 (a) Let f (z) = x² + iywhere a and y are the real and imaginary parts, respectively of z and C is a contour consisting of the line segment from z1 = 6i to z2 = 9+ 10i Evaluate Re [f (z2)] ?

Q: 12) Circle O is tangent to L: 5x - 12y + 19 = 0 and L 5x 12y 7=0. If the center of the Circle O is…

A: The given tangent lines are, L1: 5x - 12y + 19 = 0L2: 5x - 2y - 7 = 0both lines are in the form ax +…

Q: Problem IX: Evaluate |-ds where C is the portion of the curve y= Vx from the point (1, 1) to the…

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Q: Problem 58 Find the equation of the normal to the curve of f (x) = x – 3x2 at the point (1,-2). а. у…

A: Question is solved.

Q: an equation of the line tangent to the function of x2 + (y – x)2 = 9 at x = 1.

A: At given value of x find y Differentiate at given value Use equation of tangent line

Q: Problem 3. Find the shortest distance between the point P (0, 1,0) and the line l given by x = 1-t,…

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Q: An equation of the line tangent to the graph of f(x) = x(1-2x)3 at the point (1,-1) is A. y = -7x+ 6…

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Q: Find the equation of the line tangent to Y 3x2 + x + 1 at x = -3. у 3 —17г — 26 O y = 6x – 3 O y =…

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Q: Problem 3.4 Find the points on the curve y = 2x3 + 3x2 – 12x +1 where the tangent is horizontal.

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Q: 5 Find the equation of line tangent to the curve y= X+- at point P(1,3) А) 4x +у-7- 0 B None of the…

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Q: Problem 1.11 Find the gradients of the following functions (a) f(x, y, z) = x² +y³ +z*.

A: (a) Given- fx,y,z=x2+y2+z2  To find- the gradient of the above function. Formula used-…

Q: 6. Find the equation of the curve whose slope at any point (x,y) is xy and which passes through the…

A: 6. We know that the slope of the function is defined as dydx given that xy Therefore, dydx=xy or…

Q: Problem 1 Evaluate the line integral / 2* ds, where C is the line segment from (3,0) to (0,4) in the…

A: Given line integral ∫Cx2ds, line segment (3,0) to (0,4)

Q: In problem (A), find a linear approximation f(x, y) at the indicated point. (x + y)´| at (-1,1) A)…

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Q: Problem 4: For what valnes of a and o s the line y=-2x+b tangent to the parabola y=Ox° whern X=2?

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Q: problem (A), find a linear approximation f(x, y) at the indicated point. [3x – y² A) f(x,y) = at…

A: .

Q: Problem 22 Find the length of the curve defined by y=5(x-1)^(3/2)-11 from x=4 to x=10

A: Given curve

Q: Problem 5*. Find an equatic graph of: y = f(x), and para 1 f(x) = x+ 2y - %3D Vx-1

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Q: 5 Find the equation of line tangent to the curve y= x+ y at point P(1,3) A 4x - y - 7 = 0 B None of…

A: Given that: y=x+5x

Q: 13. Find the equations of both lines that pass through the point (2, – 3) and are tangent to the…

A: We need to find equations of tangent lines.

Q: find a and b if the line tangent to f(x) = a(x − b)2 − 1 at x = −3 is also tangent to g(x) = 1/4(x +…

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Q: 15. Find the equations of the tangent lines to the parabola у%3D —х2 + 5х — 6 | At its points of…

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Q: An equation of the line tangent to the graph of f(x) = -x(1 – 2x)³ at the point (1,1) is a. y = -7x…

A: f(x) = -x (1-2x)3  f'(x) = -3x(1-2x)2 (-2) + (1-2x)3 (-1) f'(1) = 6(-1)2 +1 f'(1) = 7   Slope m = 7…

Q: Problem 01: Sketch the curve: f(x) = x* - 6x²: Show complete solution and use darker/colored pen for…

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Q: 56. Use the Greek method described in Problem 55 to find an equation of the tangent line to the…

A: Solution:Given x2+y2-4x+6y+4=0 at the point (3,22-3)To find the equation of the tangent

Q: Problem 3 Find a curve in the xy-plane passing through the point (1, 3) and for which the normal…

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Q: Question 3 Let f(z) 2r-3z2-6z+2. Find the the equations of all tangent lines to f which are parallel…

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Q: 20. Find the equation of the curve for which y" = x, and which passes through the point (1, 2) and…

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Q: 3. If f(3) = 2 and f'(3) = -4 , find an equation of the tangent line when x = 3. %3D %3D А. у%3D2 (х…

A: Given : f(3)=2f'(3)=-4

Q: 1. A translation of y-f(x) through 2 units parallel to the x-axis is represented by A. y-f(x) + 2 B.…

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Q: Question 3 Let f(x) = 2r - 3x2 – 6x + 2. Find the the equations of all tangent lines to f which are…

A: we have to find the tangent line which in parallel to the line y = 6x

Q: Problem 7. Consider the Cobb-Douglas production function f(x, y) = 100/3y²/3 where x is the number…

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Q: Question 3 Let f(x) = 2x³ – 3.x2 – 6x + 2. Find the the equations of all tangent lines to f which…

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Q: 1. Find the equations of the tangent and normal lines to the following curves at the point…

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Q: The equation of the line tangent to the differentiable and invertible function f(x) at the point (5,…

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Q: 14. Find the equations of the tangent lines to the curve y = x- 6x perpendicular to the line x- 2y +…

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Q: Section 14.7: Problem 8 Previous Problem Problem List Next Problem ( , The discriminant fxxfyy-fy is…

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Q: Section 14.7: Problem 8 Previous Problem Problem List Next Problem ( , The discriminant fxx fyy-fy…

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Q: Problem IX: Evaluate -ds where C is the portion of the curve y= Vx from the point (1, 1) to the…

A: ∫xyds ds = dxi+dyj ds =dxi +12xdxj ds=(i+j2xdx ∫14xxi+J2xdx

Q: 20. Find the equation of the curve for which y" = x, and which through the point (1, 2) and the…

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Q: In Problem (A), Show that f(x, y) is differentiable at the indicated point. A) f (x, y) = (x2 +…

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Q: Problem 5 Given the function f(x) = 9 – 2x² a) Calculate the difference quotient at the two points…

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Q: b) Let f(x) = 4x - 2x - 5. %3D Find the intersection of the tangent line at c = 2 with the x axis.…

A: Given: The function fx=4x3-2x-5, To find: The intersection point of the tangent line at c=2 with…

Q: An equation of the line tangent to the graph,of f (x) = x(1– 2.x)' at the point (1,–1) is D y = 7x…

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Q: If f(2) = -3, f'(2) = ÷ and g(x) = f¯(x), what is the equa %3D the tangent line to g(x) at x = -3?…

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Q: Question 1. Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 has equation…

A: Giveny=10x+7

Q: Problem 2 1 4 If f(x,y) = 3 )==x' +¯v' -x² - 3x – 4y – 3, find the local extrema and saddle 3…

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Q: Problem 1. Evaluate x-y+z-2 ds where C is the straight-line segment x = t, y = 1-t, z = 1 between…

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Q: Suppose f, f, g, and g' have the following values: 1 8 10 3 -1 -2 -253-252-246-248-262 14 f(x) f'(x)…

A: Given table, Given equation x3+y3=f(x)g(x). The formula used are following…