-5 y = (3 — х)4 Is the following curve concave up or concave down at x= 2?

Q: Given dy (1 + 3 k). dx 13 2 What is the value of k such that y is parallel to the curve y = 3x +1 at…

A: Given,            dydx=2131+52x-32-34k            The curve is y=3x+1 at x=1.To find : The value of…

Q: 7² – 1 esec z Find the slope of the tangent lint to the curve y = /2 dt at r = 2

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Q: Consider the curve defined by z² = e²-v for z>0. At what value of z does the curve have a horizontal…

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Q: Q4] (15Marks) Sketch the curve r cose. %3D

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Q: A particle moves along the curve y=x3-x. If vx = 2 ft/sec and ax= -3 ft/sec2 as the particle passes…

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Q: - Does the graph of fo, x< 0 1. r20 U(x) = have a vertical tangent line at the point (0, 1)? Give…

A: Given: The function To check: Whether the given graph has vertical tangent line at the point (0, 1)…

Q: B-Find the point on the curve y = x + x?- 1 where the tangent parallel to the x- axis. Q 2/ La…

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Q: we draw a tangent line on y=/25 –x² at x = -3. 14 - find the slope of this tangent line. O A) 2/3…

A: To find- slope of the tangent line.

Q: Which of the following are the tangent lines perpendicular to y = x, to the curve x + y² = 8? Oy=x+8…

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Q: 1. Find the slope of the given curve at the indicated point. y= x* – 3x? + 3 at (1,1) 2. Find the…

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

Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 %3D Find y' dx a)

A: Given function is cosxy=xy-π-1 Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: (5) Find the equations of the normal and tangent lines to the curve at the point (1,2). y= =19x+59…

A: Differentiate both sides w.r.t. x.

Q: 1) Find the length of the curve; y = e" from r= 1 toI = 2.

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

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: The tangent line to the graph of y = e² at æ = 0 is perpendicular to the tangent line to y = e at æ…

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Q: Find the exact length of the curve. 1 х 3 1 s y s 2 4y2

A: Given:

Q: Find the equation/s of the tangent and normal to the curve y = x +3x–1,(1,4) a. y+4=0, 2X-1=0 O b.…

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Q: Given -옮 (1+ 올2 -3 -시, dy 3 (1+ a dx What is the value of k such that y is parallel to the curve y =…

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Q: 2 zy ら- Let Los 63 Z), find the Wニ Value of d at the point (!, Ln2, o) on the curve x = Cost , y =…

A: To find.  The value of dw/dt at the point(1, ln2, 0) on the given curves.

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: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: 7. a. Find the points on the curve x = 3(t2 – 3), y = t³ – 3t where the tangent is horizontal or…

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Q: Q3/Find the tangent to the curve x+ xy+ y' = 1 at (1,-1).

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Q: The curve y = sin I has a slope of Select one: O a. at = O b. at z = 0 . O c. Never

A: The slope of a curve at a point is the slope of the tangent to the curve at that point. The slope of…

Q: 2) Determine the points at which the following curve has the slope of 2. x = 3sin(t), y=6cos (t)…

A: We will find the points.

Q: The curves y = In x and y = 3x² have parallel tangent lines at x = A) ± √/ B) C) √6 E) 2

A: Two lines have parallel tangent if slop at the point is same.

Q: 3. What is the slope of the tangent line to the graph of y =- at x = 2? x+1 1 A) 3 B) 9e - C) 4e 4…

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Q: Given = (1 + x -- k) dy da 13 What is the value of k such that y is perpendicular to the curve y =…

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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: 23. Find the normal to the curve x2 + y² = 25 at (4,3). %3D

A: Find the normal to the curve

Q: Find the slope of the tangent line to the curve 3xy- 5y 4 at = 1. ECAD Hint: what is the y-value at…

A: Differentiate at given point

Q: 1. Make the curve y = ax°+ bx² +cx +d through (0,3) and have at (1, 2) a point of inflection with a…

A: To make the curve.

Q: :- 1 Find the interval on which the curve y = dt is concave upward. (Enter your answer using…

A: Given Data The integral is    The function of the integral in interval 0&lt;t&lt;x is,

Q: Find all points on the curve where the tangent line has the given slope. (If an answer does not…

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Q: Can there be a curve satisfying the following conditions? d2y/dx2 is everywhere equal to zero and,…

A: To check: The curve satisfying the given condition or not.Explanation:

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: 3:09 AM ...0.1KB/s at 40 < April 8, 2020 22:10 2. At what point on the curve y= 4-3e* +8x is the…

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Q: h by Delermine the longth of the Curve y=flete?) between X-0 ond X= 2

A: Consider the given curve:

Q: 2 At how many points on the curve x 3 + Y 9 in the xy-plane does the curve have a tangent line that…

A: Solve

Q: The slope of the tangent line to the graph of y =; I+1 when x = 1 is %3D %3D - 4 3/4 O 1 4. 1/2

A: y=xx+1 Slope of the tangent line is the derivative of the given function at the given point. So…

Q: y(z) along the curve given by r" = e*.

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Q: 3. Find the length of the curve given by : = (y/4)² – 2 ln(y/4) for 4 > y 2 12.

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Q: Given the curve y2º = x in the xy-plane, for what value of y, if any, does the derivative of y with…

A: Differentiation w.r.t to x

Q: Find the x-coordinates at which the tangent line 3. is horizontal to y =|1- 1. 3 Ox=-3 1. Ox-D3 O…

A: From the given problem:   y=1-3x4   As we know that the tangent line is horizontal when the slope of…

Q: -38x^8+10x^76y+y^9=-27, find the dy/dx. Now find the tangent line to the curve (1,1). Write in…

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Q: Given the curve y2" = z in the ryplane, for what value of y, if any, does the derivative of y with…

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Q: 10. For x(t)= t² +t,y(t)= e³' find the values oft where the curve is concave down.

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Q: curve that lies a. to the left of z = -1.39 b. to the right of z = 1.96 c. between z =-2.16 and z…

A: We have given that. Standard normal    X~N( μ =0 , ?= 1 )   μ =0 , ? = 1    Z-score =( x - μ )/?…

Q: ay 13) Given X = e', y=t e. Find dx and d²y dx? . For which values of t is the curve concave upward?

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.