Suppose L is the tangent line of y 3 tan a 2 csc x at x = Where does L intersect the x-axis? 40 O At x 3. 4. O At z 3/3 !! /3 // O Al 2 = - 8. O At x = O At x = T

Q: Find the slope of the tangent line at a for the graph of the f(x) = xtan z y(x) be given implicitly…

A: a) Here we have to find the slope of the function f(x)=xtanx .......................... (1)  Let…

Q: The equation of tangent line of the function 21 x3 f(x) = e7e dt %3D 21 x at x=1 is V21 e3087 (x-1)…

A: Given function is  f(x)=∫21x21x3e7t2dt Since at x=1, upper limit of the integral is equal to lower…

Q: 5m/2 sin x Applying Simpson's Rule Approximate T/2 dx using Simpson's х Rule with n = 4…

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Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: Evaluate the following integral. 2 8y sin y dx dy 0 0 İT 2 8y sin y dx dy = (Type an exact answer,…

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Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx s2n?…

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Q: B. Eind y by implicit differentiation. A.e sinh x+ In y cosh x= tanh(x - y)

A: The given equation is eysinhx+lnycoshx=tanhx-y. Calculate the value of y'. Here we use the formula…

Q: Differentiate the following functions in derivative and differential forms: f,(x) = Ax f,(x) = In x…

A: For f1(x)=Ax ⇒f'1(x)=Adxdx⇒f'1(x)=A Sketch of f1(x)=Ax limx→∞A=A

Q: Find an equation forbthe tangent line at t=1 for r(t) with r(t)=(t^3-t,sin(t-1),ln(t))

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Q: 10. Use differentials to estimate to estimate sin(46°). vZ(n+180) А. D. VZ(T+180) 360 180 В.…

A: Let y = sin (x)

Q: 4ス+S fra) = 7 +2 Contromulily of he funihim ihe fumnim Discuss The at x= 1

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Q: e the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) dx. -dx, 1+x²

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Q: Show that the function below is contimuous but not differential atr= 0. r sin() if f(r) = 0. if r =…

A: Calculate RHL and LHL

Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: hoaph fumeten nd be fure at label aut least thne f (u) : Su

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Q: 1: A)find the length of the curve y=3(x)/2 – 1 from x=0 to x=1 ? B) Prove that: cosh (x + y) = coshx…

A: A) Length of the curve is y=3x32-1 B) Trigonometric function

Q: Find the slope of the tangent line to the graph of x²-Iny=0 at x=2 O None of these O 4e4 O e4 O 4

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Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Suppose L is the tangent line of f (x) = csc T at x = 2 . Where does L intersect the y-axis? Note:…

A: We have to find

Q: d mula sinh (t) = In (t + VE? + 1) and- (In(t)) = } %3D ne derivative of sinh(t).

A: Here we use rule of differenciation to find the required derivative.

Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In () (Inx)2+ (In Vx)3 3* 2) y = tan-1 (x*)

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Q: Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In'…

A: This question is based on diffrentiation.

Q: please show all steps

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Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

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

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: 35. Does the graph of Sx*sin(1/x), x + 0 f(x) (o. x = 0 have a tangent line at the origin? Give…

A: Given: fx=x2sin1x,x≠00,x=0

Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

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Q: Find dy Ldx For the following (Jy)' =(In tan x)(x") ( sin x)"

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Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

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Q: Find an equation of the tangent line to the graph of f(x) = | t cosh (t² – 1) dt tan-lt 1+In (x) at…

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Q: The derivative of y=eov? +cosh/x equals Select one: O y' = 2/x et +sinhx + sinh/x O None O y'=@ov +…

A: This is a composite function. Therefore we have to use rules for derivative of composite functions.

Q: 9. What is the derivative of cos(at5 + b) with respect to t?

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Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

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Q: Find the length L of the arc formed by y = (-0.5x2 + 16 In(x)) from x = 4 to x = 6 %3D •6 Set up: L…

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

Q: (f) y = e* In(tanh(x))

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Q: 1)Find dy/dx for following functions. 1) y = (In 4)* + In A + (In V) (Inx)2 2) y = tan (x*)

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Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

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Q: 1. Find for differentiate each of the following functions. dy хр a) (In(coshx) sinh x) g) y = - b) y…

A: Given: a)lncoshx3c)y+4coshx2=exsin-1(2x)g)y=sinhxex

Q: Evaluate / (2x – y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) 11760/7 X

A: Explanation of the answer is as follows

Q: The slope of the tangent line to the graph of y = ln x at x = a E R approaches infinity as a → 0+.

A: Given curve: y=ln x

Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(x) = 1 In r 2 - 4* where…

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Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: s the indefinite integral | x2 cos(x3) dx becomes 1 cos(u) du- must also convert the integral…

A: Given query is to find the integral limits.

Q: 3. Evaluate the following derivatives: a) y = In[sinh(2x)] b) f(t) = tanh-1 VE

A: Derivative of the inverse hyperbolic function formula: -  ddx(sinhx)=coshx ddxtanh1x=12ln1+x1-x…

Q: - 322 - 4x - 5 Set up but do not evaluate the integral to find the length of the arc of the curve y…

A: Given query is to find the integral form arc length.

Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration