1. z dz along a straight line parallel to the x axis. (1 + i

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: Given that y =5u'+4u and x 1 hence find dy dx

A: Differentiation problem

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: 4. Evaluate: S. yx?dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t2 , (0 st< 1).

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Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: 3. (x² + 6y²)dx – 4xydy = 0 , y(2) = 1

A: Problem is in the form of homogeneous form...so put y=v.x and proceed as I have done solution step…

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: 2. Eliminate the parameter and find the equation of the curve in x,y Curve: x=1-sin?t, y= cost, 0 <t…

A: topic - equation of curve in x,y

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

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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: Evaluate: S. yx2²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: y to solve the following linear differe ] dy

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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: 4. Evaluate: S. yx²dx + xzydy + xz?dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

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Q: Use a computer algebra system to plot y2 = x 3 - 4x for x and y between -4 and 4. Show that if dx /…

A: y2=x3-4x

Q: 2. Find the lengths of the given curves: a) y = x/2 -x2,1sK< 4 L = V1+f(x)*dx 3

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Q: 1. Solve the DE as follows: d'y dy +3 +2y = 24 y(0) = 10 and y'(0) = 0 di? dt

A: Given differential equation  is   y"+3y'+2y =24    ;    y(0) =10     , y'(0) =0

Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: Given the equation 2= 3x2 +1 with y(1) = 2. Estimate y(2) by Euler's method dx using h = 0.25. %3D

A: Note: Hi there! Thank you for posting the question. As there are several independent questions,…

Q: B) Find the general solution to the following DE. dy y? + x2 = 0 dx

A: Given differential equation is y2+x2 dydx=0

Q: re poinit Cur 8X° + 22X 24X e tangent line is parallel to the x-axis? . (1,0) (2,1) (3,0)

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Q: 69) 21) The tangent line of y = In(x² - 8x + 9) is horizontal at x = A) – 2 B) 2 C) 4 D) – 4

A: Given that: y=ln(x2-8x+9)

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

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Q: 3. Find the slope of the tangent line to the curve y = +2 x*+4x+7 4. Determine and 4 of y = (5.x² –…

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Q: d the equations of the tangent and normal: 2xy + 5x – 9y = 0 at x = 4.

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

Q: dy is equal to- dx If y = !, then the value of +3 V1 +y* V1+x

A: Introduction :

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: Express æ = e-t, y = 2e2" in the form y = f(x) by eliminating the parameter y =

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Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

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Q: .4. The approximate value of y=V4+sin.x at x=0.12, obtained from the tangent to the graph at x = 0,…

A: 14)  y=4+sin xy=4+sin x12 Differentiate with respect to 'x' As,  dxndx=n xn-1d sinxdx=cos x…

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: 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: Lind -2x+H where X- oro Zy

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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: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &amp;  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

Q: S, (x + 2y) dx + x dy. C consists of line segments from (0. 0) to (2. 1) and from (2, 1) to (3, 0)

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Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

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: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: 1- y? 1+ y 4 06: If x? dx Show that 1 %3D ,2 dy レアス+1.

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Q: Which expression gives the length of the curve y = 4x from x=1 to x = 4 ? 4 (A) [ 4x°dx (B) |V1+4x…

A: Given query is to find the expression for length of the curve.