EXAMPLE 2 Vertical and horizontal tangent lines Find the points on the interval -TS0 S T at which the cardioid r = tangent line. f(0) = 1 – cos 0 has a vertical or horizontal

Q: 7- 6- 5- y = g(x) 4- 3- 2- 1. 1 2 4 6. 7 The figure above shows the graph of the differentiable…

A: Given problem:-

Q: sin x Let g(x) = . 1 Find the derivative a'(x). dt . 2 1+t3 cos? x 1+ sin x sin x 1+ cos³x cos X 1+…

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Q: I(x) = 3 esin(x) ga = 3 cos(x) esin(x) a) Find the equation of the line tangent to the graph of g at…

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Q: Evaluate the limit.

A: Given limit: limh→0 sin2h sin3hh2

Q: (sec x). What is the slope of the tangent line to the graph Let f(x) = tan of f at the point = 0?…

A: 1.

Q: Tangent lines Find an equation of the line tangent to the cycloidx = t - sin t, y = 1 - cos t at the…

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Q: Assume that functions f and g are differentiable with f(-5)% = -4, f'(-5) = -4, g(-5)= -3, and…

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Q: Excrcise 4. Sketch the graph of function y = x sin(In(x)) a) Identify the domain of function and any…

A: Given function is y=xsinln(x) Graph of function is a: Since ln(x) is only defined for x>0, so…

Q: If Z= arctan ), find 2

A: Formula Used:

Q: 3-10 - Slope of a Tangent Line Find the slope of the tangent line to the graph of f at the given…

A: fx=3x+4 at 1,7slope=ddxfx=ddx3x+4                     =3Slope of the tangent line to fx at the…

Q: 1. Using Cauchy-Riemann equations find the derivative (i.ef'(2)) of (a) f(z) = 2². (b) f(z) = e².

A: As per our guidelines, we are entitled to answer only one question at a time. So, please re-post the…

Q: Using a Tangent Line The tangent line to the graph of y = g(x) at the point (4, 5) passes through…

A: Given that there is a tangent line to the graph of y=gx at the point 4,5. Therefore, 4,5 lies on the…

Q: QI- 1) Show that cosh²x – sinh?x = 1 ii) Find the equation for the tangent line to the curve y = V+1…

A: By using the definition of hyperbolic functions in terms of exponents we solve (i) .  And by using…

Q: 5. [-/1 Points] DETAILS SCALCET9 3.5.027. Use implicit differentiation to find an equation of the…

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Q: termine the absolute maximum and minimum values of f(x) = cos²x-cosx the interval 0≤x≤ 2π.

A: Given that fx=cos2x-cos x, x ∈0, 2π To determine:  Absolute minimum and maximum. Needed formulae:…

Q: 8. h (х) — 9 — 8 sin on [-3, –1]

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Q: function f(x) = x² ose x-coordinates are -2 , 0, and 1. 2x and draw the tangent lines to the gr 10 4…

A: We will draw the graph and the tangents.

Q: 7 sin x Let f(x) 6 sin x + 2 cos x Then f'(x) = The equation of the tangent line to y = f(x) at a =…

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Q: Tangent Line. If p(x) : 2x2 + 6х3 + + 4 (a) Then p'(1) = (b) The equation of the tangent line to the…

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Q: = -4 and g'(2) = 3. (Enter your answer as an equation in Find an equation of the tangent line to the…

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Q: Exer. 1-6: (a) Ure Definition (2.1) to find the slope of the tangent line to the graph'of ƒ at P(a,…

A: 1. (a) Consider the given function, fx=5x2-4x the slope of the tangent line to the graph of the…

Q: D. Implicit Differentiation Assume that z is a function of x and y, find Zx if xz + ylnx = z2 – sin…

A: We have to find the Zx.

Q: 24 Find the tangent line to y x-x+2 at x 2 2 x-x+2 at x The tangent line to y 2 is y

A: At x=2 we find y first y=2So the point at which there is tangent is (2,2)

Q: IVIC Question 8 of 10 y The tangent line to the curve y=f(x) at r=1 goes ough the points (-1,3)…

A: To find out the value of f(1) and f'(1).

Q: Implicit Differentiation (a) Find dy of (x*u2 )*= 2xy at the point (1,1)

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Q: [cost- sin t Q2) Determine whether x, = ,X1 = |cost| and x, = Lcos t] Co t sin t| are linearly…

A: For linearly independent , determinant of matrix should be non zero.

Q: 7 sin x Let f(x) 6 sin x + 2 cos x 7. Then f'(x) = 2(3 sin(x) +cos(x))- + cos (x The equation of the…

A: Given:-f(x)=7 sinx6 sinx+2cosxf'(x)=7 33sinx+cosx2To find : the equation of tangent line at x=π2

Q: sin πx , x 2. 4 If the function f(x) is continuous at the point x= 0. then what is the sum of…

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Q: Tangent lines Find an equation of the line tangent to the curve at the point corresponding to the…

A: Given curve is x=et and y=lnt+1 To find: The equation of tangent line at t=0 Solution:…

Q: ACTIVITY 3: THE IMPLICIT DIFFERENTIATION Direction: Find Dy by implicit differentiation for the…

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Q: EXAMPLE 7 Finding Differentials of Functions (a) d(tan 2.x) = sec² (2.x) d(2x) = 2 sec2 2x dx (x +…

A: (a) dtan 2x=sec22xd2x=2sec22x Hence the answer.

Q: EXAMPLE 1 Finding antiderivatives Use what you know about derivatives to find all antiderivatives of…

A: Given: I1=∫3x2dx, I2=∫dx1+x2, I3=∫sintdt we know that  ∫xndx=xn+1n+1+c…

Q: z – i Differentiation. Find the value of the derivative of at i. z + i AL- - 12 z=i

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Q: 2y3 8. lim y-0 y-siny 9. lim(secx + tanx)csc X+0

A: To Find: 8. limy→02y3y-siny9. limx→0secx+tanxcscx

Q: 1. Calculation of derivatives: Show that cos' z = – sin z, sin' z = cos z by using definitions (a)…

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Q: ACTIVITY 4 DERIVATIVES OF TRAMSCEN DEMTAL FUHCTION ý FIND THE DERIVATIVE OF EA CH FUNCTIOM SIMLI FY…

A: We will use Chain rule and product rule of derivative along with derivative of standard function. As…

Q: 6.) eat cosh (be)

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Q: 2 points is The second derivatives of the function y = None of them d) dx b) = 2+ O A O B O D O E 2…

A: Given the function, to find first and second derivative wrt x.

Q: estion 3 i) Find all points on the curve x(x + y²) = y where the tangent line is parallel to the…

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Q: Explain why or why not Determine whether the following state-ments are true and give an explanation…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: Find the absolute maximum and absolute minimum values of f on the given interval.   f(t) = 2 cos(t)…

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Q: 2. Computing Derivatives; Compute each derivative using the derivative rules: d (a) (cos-(1+ 2*) +…

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Q: 2. The normal line to a graph of a function f(x) at a point x = a is the line that passes through…

A: Tangent line equation is, Y =MX + C Normal line equation is, Y = M'X + C Where, M' = -1/M

Q: ind the equation the tangent line and normal line to the graph of f(x) = x³ at x = 2.

A: Given f(x)=x3 substitute x=2 in f(x)⇒f(2)=23=8 The tangent line passes through the point (2,8)…

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 20-x²;…

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Q: COS 9. Prove cost - sin* t =1 - cos t - tan²t

A: We have to prove that  (cos4t - sin4t ) /cos2t  = 1- tan2t

Q: A function H is differentiable at x = 1. An equation for the line tangent to the graph of H at x = 1…

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Q: sin 3x . [T] lim S.M; x→0 ; ±0.1, ±0.01, ±0.001, ± 0.0001 sin 3x sin 3x X -0.1 а. 0.1 е. -0.01 b.…

A: Evaluate the limit for x→±0.1limx→-0.1sin 3xx=Sin 3x-0.1-0.1                    =-Sin0.3-0.1…

Q: 75. Derivatives from tangent lines Suppose the line tangent to the graph of f at x = 2 is y = 4x + 1…

A: The line tangent to the graph of f at x=2 is y=4x+1.