Consider the unit circle centered at the origin and with a vertical tangent line passing through point A in the accompanying figure. Assume that the lengths of segments AB and AC are equal, and let point D be the intersection of the x-axis with the line passing through points B and C. Find the limit of t as B approaches A. в,

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A: Answer: f'(-2)=-1

Q: Find the limit (if it exists).

A: If the vector valued function is of the formr(t) = f(t)i + g(t)j + h(t)kThen its limit is given…

Q: Show that if 0 ≤ f' (x) ≤ 1 for all x, then the arc length of y = f (x) over [a, b] is at most √2(b…

A: The arc length increases with the value of f'(x) Means, if f'(x) increases then arc length will…

Q: Given circle Z with tangents XW and XY, what is measure of arc WVY

A: We need to find measure of the arc WVY. We shall use the relation between Circles and angle between…

Q: Use the arc length formula to show that the length of a linear function f(x) = mx + c on the…

A: Let f(x) be a function over the interval (a,b), Then the arc length of f(x) from the point (a,f(a))…

Q: In the given figure, CF and BF are tangents to crcle A and intersect at F, a point on circle E. BF…

A: Given Figure:

Q: Find the tangent line to the given circle as directed. x² + y² + 10x – 6y – 2 = 0 parallel to y =…

A: Equation of the circlex2 + y2 +10x -6y -2 = 0⇒x2 + y2 + 10x -6y -2 + 25 - 25 + 9 -9 = 0           .…

Q: Find the limit (if it exists).

A:

Q: By computing the limit of right-endpoint approximations, prove that b4 x' dx 4 if b > 0, then

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the limit if it exists.(Use squeese Thcor lim Cx,y)>(0,0) x²+5y²

A:

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

A: f(x)=x3, a=-2

Q: If one uses the horizontal strip/element as a representative area, then the infinitesimal change may…

A: The area of the region under the curve can be calculated using the horizontal or the vertical…

Q: Find the limit for the following lim y→0 sin(3y).cot (5y) y.cot (4y)

A: I use standard limit results

Q: Evaluate the limit, using L’Hôpital’s Rule if necessary.

A: The limit of a function limx→Xfx=Ymeans that value of  function f(x)f(x) can be as close to Y by…

Q: Let A be the area of a circle with radius r. If = 2, find when r = 3. di dt

A:

Q: If C'is the circle of radius 3 centered at the origin, starting at the point (3,0) and moving around…

A: Answer and explanation is given below..

Q: Use l’Hôpital’s rule to find the limits

A: Given: limt→0sint2t To determine:  The value of given limit using L' Hospital's rule. Concept used:…

Q: 11. 12

A: 11. The figure of the circle is given by To evaluate : The value of x

Q: If two circles are concentric and a chord of the larger circle is tangent to the smaller circle,…

A: According to given,

Q: Let (a, b) be an arbitrary point on the graph of y = 1/x, x > 0. Prove that the area of the…

A: The given function for the curve is, y=1x The slope (m) of the tangent at the curve is,…

Q: Find the limit (If it exists). (If an answer does not exist, enter DNE. Round your answer to four…

A: This question can be solved using the concept of limits.

Q: f(x, y) = e¬aY sin(x + y) (г, у) —> (1, -1). as

A: We will plug the limits in function to find limit of function

Q: Which best describes a removable discontinuity at x = a using limits? m flm) deog not ovist

A:

Q: Being f(x,y) = xy + y^2, find the following limits:

A:

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

A:

Q: Aetermine whather im sin y exicts If it exists, find the limit ?

A:

Q: Use the distance formula to show that T (x,y) = (-y,x) is an isometry.

A: We have to prove that T(x, y) = (-y, x) is an isometric.

Q: Use l’Hôpital’s Rule to find the limits

A:

Q: Evaluate the limits at the indicated values of x and y.

A: This question is related to limits, We will solve it using given information.

Q: Find the limits. Enter "DNE" if the limit does not exist. lim (1,y)→(7,6) Vy DNE 1 lim (z,y)→(9,4)…

A: we have to find the following limits

Q: A circle, with area A = tr“, is expanding with time. dA = 6 cm 2/s, what is dt dr when r = 2? dt If…

A:

Q: 8. Find YZ. 2r + 12 10 W r+3

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

Q: Select which of the following meets the given description. Tangent line GE has a point of tangency…

A:

Q: AC is tangent to circle O at point C. What is the measure of AOC?

A:

Q: From the vertex (0, c) of the catenary y = c cosh(x/c) a line L is drawn perpendicular to the…

A:

Q: Evaluate the limit using L'Hospital's rule lim 7re – 7æ I+ 00

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x−1, a…

A:

Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

A:

Q: Use L'Hospital's Rule to find the limit as z approaches i of (1 + z^6) / (1 + z^18)

A:

Q: Prove that the lengths of the two tangent segments to a circle from a point outside are equal. Use…

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

Q: Compute each of the following limits. Use exact values. |- 40 8y lim V -5 y + 5 40 – 8y lim %D y + 5…

A: -40-8y=--40-8y   if  y≥-5-40-8y        if  y<-5 Now,…

Q: V16 + h – 4 lim h>0 h

A:

Q: Find the following limit if it exists, or show that the limit does not exist, y? sin? x lim…

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

Q: Let sin(2t) F(t) = + cos t, Find the limit lim F(t).

A: We have to find the limit

Q: Find the limit of the following function. а sin (aтz) dz

A:

Q: nd the length of a tangent drawn to a circle of radius 3.2cm from a point which is 5 cm away from…

A:

Q: A circle, with area A = Tr2, is expanding with time. dr If = 6 cm 2/s, what is dt dA when r= 2? dt…

A:

Q: If C is the circle of radius 3 centered at the origin, starting at the point (3, 0) and moving…

A: -81π/2