%3D i) Find the tangent line to f (x) = tan x + 9 cos x at x = T

Q: Find the equation of the tangent line to the curve y = 5x cos T at the point (T, – 57). The equation…

A: Please refer the attached image for complete solution. THANK YOU.

Q: What is the range of the tangent function y=tan(x)? A R B [- 1, 1 [0, + ) D (- 00, 1]U[1,+ ∞)

A: Tanx is the ratio of sinx and Cosx

Q: dy using implicit differentiation. dx 3. Find sec (xy?) = (cosh )(tanh a+/Ð) + 2 csc-' (tan(y + 1))

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below y = Arctan…

A: Given     y=tan-1(sec(3x))+π(cot(2x)

Q: An equation for the tangent line to the curve In(sec x + y?) = tan(x)+e2" – 1 at the point (x, y) =…

A: Given curveIn (sec x +y2) = tan x +e2x-1We have to find the equation of tangent line at the point…

Q: Find the derivative. sin 0 d. 1 dx 1- x2 de A. tan 0 B. sec 0 C. cot0 O D. cos 0

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Q: PCtrrminc Arc Lengtn. X= 3 sin(t) y= 3 COS (t)

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Q: The exact value of the slope of the tangent line to the graph of the curve r = 9 + 8 cos(e), at e =…

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Q: Determine the equation of the curve whose tangent line at any point (x, y) is e*- cos x and passes…

A: The curve whose tangent line at any point x,y is ex-cos x and passes through 0,4

Q: dy Use implicit differentiation to determine dz given the equation zy + cos(z) = e".

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Q: S cos*x sinx dx

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Q: Find the slope and the rate of change of the slope with respect to x when x = 2 cos (3t) - 3 sin(2t)…

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Q: ind the slope of the line that is tangent the curve sin(2x)+sin y=e*y – 1 at (0,0). our answer…

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Q: Use a computer algebra system to plot y2 = x 3 - 4x for x and y between -4 and 4. Show that if dx /…

A: y2=x3-4x

Q: dy Find the derivative, y' = dx , of y = sin(cos(tan(sec(csc(cot(x²))))))

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Q: Find dy/dx by implicit differentiation. (sin pix + cos piy)8 = 12

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Q: Find dx when x = 0, if given y = tan¬ (sinh r).

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Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: nd the equation of the tangent to the curve y = 2 sin x+ cos 2x at the point x= 7.

A: equation of line at point (a,b)  is given by    y-b = m (x-a)  Where m is the slope of tangent  As…

Q: Find the derivative. sin t du 4-u? di cost OA. 4- sin?1 O B. cos t(4- sin ?1) OC. 4- sint - cost O…

A: We need to find the integration of given expression.

Q: Consider f(x)=tanx a. Find the linear approximation of f(x) at a=pi/4 b. Use this to estimate…

A: This question can be solved using the formula of linear approximation.

Q: A one-meter long bar is heated unevenly, with temperature in degrees Celsius at a distance a from…

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Q: e cos at the Find the equation of the tangent line to the curve y = point (e?, 0).

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Q: tanx +y = 0 dx

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Q: S sin'x·cos'x dx

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Q: Find the lengths of the curves x = ln (sec t + tan t) - sin ty = cos t, 0 ≤ t ≤ π/3

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Q: Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not…

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Q: The derivative dy for the function %3D (1i) y= cot リーCof V-x

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Q: If x cos' 0 y = sin' 0 dy • the derivative dx and %3D (A) tan' 0 (B) -cot 0 (C) cot 0 (D) -tan e (E)…

A: Given: x=cos3θ and y=sin3θ To find: The derivative dydx

Q: Q3: dy\dx of f(x)= tan x cot x is

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Q: 15. Find the derivative. (a) f(0) = arcsin 02 %3D (b) h(t) = arctan(e*) %3D

A: Given:- (a) f(θ) =arcsin(θ2)  (b) h(t) = arctan(et)  To find:- Derivative of given functions

Q: 1.) The slope of the tangent line to the wve y?= 5+-1 at PCi,e) 2.) Find the First denivative of…

A: Using derivatives.

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

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

Q: xcos( x), sin(x) 8. dx = LHIN

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Q: Find dy/dx using implicit differentiation a. tan y=x+y b. cos x=x(1+cot y)

A: For (a),     tany=x+yDifferentiating both sides we get,⇒sec2y y'=1+y'⇒dydx=1sec2y-1

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: Q2- Find for the following function :- dx 1- y = sinh-(tan x) – tanh-1(sin x)

A: We will differentiate using direct formula and chain rule.

Q: 3n Find an equation of the tangent line to y = 7 sin(x) at x = .

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Q: Find the derivative. sint 1 du 1-u? dt cost OA. 1- sin? t 1 OB. OB. 1- sin?t 1 Oc. cost (1- sin 2 t)…

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Q: Find the equation of the tangent line to the curve 1 y = 3 sin z + 4 cos a at the point (0, 1/4).…

A: Given:     y = 1 / ( 3 sinx + 4 cosx ) Point: ( 0 , 1/4 )

Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Given,         x=t-sint , y=1-3cost , t=π3

Q: dz i. y = e? sin x + In x (arcsin z) with = 4 dx

A: It is given that,  Therefore now take the derivative of the given function. So,

Q: Q1- i) Show that cosh?x – sinh?x = 1 ii) Find the equation for the tangent line to the curve y = Vx…

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Q: Which of the following is the slope of the tangent line to f(x) = cos(ax), a E R at x = T? 1 а 1 а

A: Given equation is f(x)=cos(ax) at x=π Find the slope of the tangent line

Q: Given the function In (x +y)+ tan (2xy) y -3x4. Find dy using implicit differentiation. dx

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Q: H.W Ex.(8) Show that the functions f(x) = sin' () and ga)=2 tanv メ+) have the Same derivative.

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Q: Find dx and simplify whenever possible. 1-cosh x 1. у 3D 1+cosh x 2. y = x tanh¯x + In V1 – x²

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Q: QS:-Find the first order derivative of each of the following functions: a) y = etan"x + In (sin-x)…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.