1. Find the line L passes through the point (1,2) and parallel the line L': x + 2y = 3.

Q: Suppose C=D0, so that 23 24y 5x3 = 0. Find all points (x,y) at which the tangent line to the…

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Q: dy Find dæ Given that y = 3u² – 7u + 5 and u = 6a² + 4x – 1. 1. 2. Find an equation of the tangent…

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Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

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Q: 1. Differentiate G(x) = Ax+Bx+C 2. At what point on the curve y= 1 + 3e* – 3x is the tangent line…

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Q: Find without using the Chain Rule and the ProductRule

A: We simplify the inner function using the properties of log.

Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…

A: " Since you have posted a multiple questions, we will solve first question for you. To get remaining…

Q: Given that the line y= 2x +c is a tangent to the curve y = kx, where c and k are positive constants…

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Q: Find an equation of the tangent line at x= a. x- y%3D a = 2 4 10 A. y=x+1 *B y=x-1 y3x-1 Xe y=x+2…

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Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…

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Q: Find the length of the curve y2 = ln x, -1 ≤ y ≤ 1.

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Q: Given f(z) = x+ VE Calculate the tangent line at the point (16, 20) y : (2- 16) + 20

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Q: Use the Chain Rule to find dz/as and dz/at. 2 tan(u/v), u = 5s + 2t, v = 25 - St

A: Proceed as shown

Q: IF. dr where C is the line segment from ( C (yz) + 1)i + (xz cos(yz) + 2y)j + (xY cos

A: The answer is 88

Q: Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

A: To Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

Q: The equation of the tangent line to the curve y = 1 at the point (3,-) is Vx +1 A. x+16y +11=0 B. x+…

A: Please refer the attached solution. None of the option is correct here . I have solved it…

Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

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Q: 17. The equation of the tangent line to the curve y = at the point (3, ÷) is 2 A. x+16y+11= 0 B.…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: 17. If the curve C is given by x= 3t² +1, y=4t, z = e, find the equation of the tangent line at the…

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Q: Let f(x) =- 3x – cos-1(x), then the equation %3D of the normal line to the curve at the point (0,0)…

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Q: Find the equation of the tangent plane to z=e^y+x+x^4+6 at the point (4,0,267).

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Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: What is the equation of line tangent to sin r+1 y = at the point (T, -1)? cos E O y= TX –1 - O y = 1…

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Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: Find the equation of the tangent plane to z = e + x + x³ + 9 at the point (2, 0, 20). z =

A: According to question We have to calculate the equation of the tangent plane .

Q: 11.What is the slope of the tangent line to the curve y = 3x? – 5 at poin - O A. -7 О в. -5 O C. -6…

A: Differential equation

Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

Q: 20. The curve 2x2y+ y 8x +1 passes through (4, 1). Using the tangent line to the curve at the point…

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Q: evaluate the integral over this curve

A: This question is taken from the vector calculus in which we have to find the line integral of the…

Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…

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Q: Find all points on the curve e = {{r,y) : x² – ry + y? = 7} where the tangent line to C is…

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Q: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

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Q: Find the equation of the line tangent to y 8xe" at x = 1. O y -8e = 16e(x – 1) O y - 8e = 8e(x – 1)…

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Q: În 10 In 10 (2x- 7) 2 IH 10 Find the indicated tangent line. 17) Find the tangent line to the graph…

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Q: A curve is defined implicitly by the equation x²+xy+y³=1 dy Differentiate implicitly to find dx

A: Follow the procedure given below.

Q: 8. Consider the curve given implicitly by -x2 + 3xy+2y² = 2 y. 8.1. Verify that (1, –1) lies on the…

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Q: Given x = 2 lnt and y = 1+t, find the equation of the tangent line when t = 2. %3D O y=-4x-8ln(2)-5…

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Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

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Q: The parametric equations of a curve are given by x = In (Vi +1) and y = cosh (2t). dy Find the…

A: Use chain rule of differentiation to solve this problem.

Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: The tangent line to the curve y=vx-5 * for x=16 is a. y=1/8 (x+16). O b. y-4=1/6 (x-16). O c.…

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Q: 2. Find for the curve dx x²y3 – 2xy = 6x² + 2y³ + 1 -

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Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: 3. Find the value of c such that the line y = x + 3 is tangent to the curve y = cvx. C =

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Q: 3 If the length of the curve y = 4 xž from the point (0, 0) to the point (xo, f(xo)) is L = ((20737)…

A: Given,          The length of the curve y=4x32 from the point 0,0 to the point x0,fx0           is…

Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

Q: 3. Find the equation of the tangent line to the curve at (1,2) * y = 5 - x O A. x-6y + 22 = 0 O B.…

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Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: