#4) What valwes of c Cif anu) are predicted by the Me an Vae Thearem for the function fex) = (x-32)o an the interval [0,2]?

Q: 6. Find the shortest distance from B6,0,0) to the pane Ax + By tCz +D= 0 where A, B,C and D SR .

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Q: Find the set on which the curve is concave upward. Answer (in interval notation): | 2 y = ₁² 1²+ 3²…

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Q: a bounded by the curve y = 3VI and the lines z = 6 and z= 8 above the z – azis is Võ+ 12v6 O 10

A: We have to choose the correct answer

Q: Consider the curve segments: 1 - to x = 4 and 3 1 to x = $1: y = x² from x S2: y = Vx from x = = 16.

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Q: A line is tangent to the curve y = 3x1 and is bounded by the r- and y-axis in the first quadrant.…

A: Let's find.

Q: Which of the following is a parameterizatino of the line that passes through the point (5, 4) With a…

A: Let's find.

Q: 3. Describe the level surfaces of the function. f(x, y, 2) = x² + 4y? + 42?

A: We Know that,  A level surface of a function w = f(x, y, z) with three variables is a surface f(x,…

Q: is concave up on interval The graph of f(x)= x2 – 1 OA(-1,1) OB (0,1) oC(-1.0) U (1, 00) OP (-x,-1)U…

A: F is concave up if f’’(x) > 0.

Q: 2. Find the angle of intersection between the following pairs of curve. Express your answers in…

A: We know that; The expression for the angle of the intersection between the two curves is:…

Q: x?y" – 4xy' + 6y = 0, y(-2) = 8, y'(-2) = 0

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Q: Find the set on which the curve 7 dt t2 + 6t + 15 y = is concave downward. Answer (in interval…

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Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: Calculate f. x²dx + xydy where C consists of the straight line segment from (0,0) to (1,1), followed…

A: Proceed as shown below

Q: A curve through the point Q(4,3) has the property that the sum of the distances from each point on…

A: The distance between the points and is given by the expression . If 2 lines are perpendicular,…

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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Q: ,is concave up on interval x2-1 The graph of f(x)D OA (-1,1) OB. (0,1) В. Oc. (-1,0) U (1, 0) OD.…

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Q: Suppose that you are climbing the Gua Singa, with the shape given by equation Bxm + Cy" – Dx – Ey +…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: Find the artho gon al traje eteries to c°y" - 4y + x*

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Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

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Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

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Q: 2. Approximate f,(3,5) using the contour diagram of S(x, y) in Figure 14.9.

A: Given query is to find the value of fx(3,5).

Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: 4. The tangent of the acute angle between the linesy = 4x – 3 and y = x - 5 is Tano 144() 13 3

A: Please rate

Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

Q: Find the point(s) of intersection of the curves r = 10 and r = 20 cos e. O A. (10,5) 3 OB.…

A: Given: r = 4  r = 20 cos θ

Q: Determine whether the work done along the path C is positive, negative, or zero. y zero positive…

A: Ans:

Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: 3e) if c is any Simple Closed Curve, evaluate f dz, if ü7is out side (ii) 7 is in side

A: We will solve it by Cauchy Residue Theorem ∫f(z) dz = 2πi×R where R is the Residue of the…

Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

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Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: Determine the interval(s) where f(x) = 12 + 2 is concave up a) O (0, 0) b) O(-∞, 0) U (4, ∞0) c) O…

A: when the second derivative is positive , the function is concave upward. when the second derivative…

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

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Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

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Q: Evaluate F. dr where F(x, y, z) = (3.75yz cos(xyz), 3.75xz cos(ryz), 3.75xy cos(xyz)) and C is 1 1…

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Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

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Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

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Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

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Q: 1.) If the ball 1s Thrown vertically upward with a Veloorty of 15 m/s then ts heioht aifter t…

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Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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