In each part, choose the letter from the dropdown menu that corresponds to the most accurate description of the given statement. 1. -3 dr A. An antiderivative of y = -3 v 2. -3 dx B. A family of functions whose derivatives are y = -3 C. The net area bounded by y = D. The derivative of the function y = -3x – 6 3 on the interval [-2, 3] 3. (-3x – 6)' E. None of the above 4. -3x – 6

Q: Use differentials to find the value of  GIve anser to two decimal places.

A:

Q: (Tlog3(cosh z) + csch x) tanh x dx

A: Here we have to integrate the given Integral

Q: 8) Find all values of t for which x = +5, y = t lnt – t has a vertical tangent line

A:

Q: Find the firs t derivative of the f anction y=4sin[sselur)] at the Point x= T

A:

Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

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 the antiderivative for each function when C equals 0. Check your answers by differentiation. 7…

A: Integrate. ∫hx=∫sec2xdxHx=tanx+C=tanx+0=tanx   Check by differentiating. ddxHx=ddxtanx=sec2x…

Q: Find the absolute extrema for the given furction 32 flz) =6+2r+ on each of the below intervals: (a)…

A: Consider the function f(x)=6+2x+32x   (a) To find the absolute extrema on the interval [-1, 6],…

Q: Note that the solution of the DE: y(x) = e* (S e*~*dx +C) contains an anti derivative which has no…

A: Note: As there is not any point as d. So we cannot solve question h.. Here is the solution of f…

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: The volume of a right-circular cone of radius r and height h isV = π/3 r2h. Suppose that r = h = 12…

A: Consider the given: Volume,V=π3r2hr=h=12 cmDifferentiate w.r.t. "r",dV=π32rdrh    ⋯⋯11cm increase in…

Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

A:

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a ,b],…

A:

Q: The volume of a right circular cylinder with radius r and height h is V = πr2h. Is the volume an…

A: Given: Volume of a  right circular cylinder =  πr2h  To determine: Is the volume an increasing or…

Q: Suppose that y is a differentiable function of x andz = cos (x4y9).Express  dz dx  in terms…

A: Given a differentiable function

Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: Find dx for y = Vx-7 by using the definition and then rationalizing the numerator. For what values…

A:

Q: The tangent lines which was drawn at points A and B on the following y = f(x) function graph are…

A:

Q: B. Eind y' by implicit differentiation. Lesinh x+ Iny cosh x = tanh(x - y)

A:

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

A:

Q: -√x Q3. Change the order of integration and evaluate f* f* dy dx.

A: We can solve as follows

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

A:

Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

A:

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: 2(z–1) sinh z cosh I + 3(x – 1)'sech? (z)? Which among the choices will result to a derivative of O…

A:

Q: 3. Use the first derivative to find the location of all local extre ma for the following functions.…

A: Explanation of the answer is as follows

Q: 5.Differentiate.   y=3/2−4x

A: We will differentiate using chain rule of differentiation.

Q: 8. What is the derivative of y= Vu in terms of x? dy a) 2/y dulas b) 2vu d) 2/u

A:

Q: Recall that the volume V of a circular cylinder with a base of radius r and height h can be…

A:

Q: Choose the Correct answer for the following: dy 1- dx for y - sech' x is equal to: a) sech x tanh x…

A: Chain rule of derivative: ddx[u(v(x))]=u'(v(x))×ddxv(x)   Given function is: y=sech3x

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

A:

Q: Choose the Correct answer for the following: dy 1- dx for y sech x is equal to: a) sech3 x tanh x b)…

A:

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

A:

Q: Differentiate the given function: y = In(sinh(2 z)) a) О sinh(2 ¤) 2 cosh(2 ¤) b) O sinh(2 z) 2…

A: Using the identities,         d( ln( x))dx=1xd(Sinh (x))dx= Cosh xd (ax)dx=a

Q: Q2 / Find dy/dx for the following functions; 3 1. y = Vtan(sin(x² – 1)) d 2. ((1 + cot x)³) dx x². d…

A: To find dydx differentiate 'y' with respect to 'x'. For the given values of 'y' we have to find dydx…

Q: C) use implicit nind ay differentiation to dn for 22 (Osh (y) - In (tanh 2) = y2 %3D

A:

Q: Find the interval on which the curve 1 dt 6 +t + 2t2 y = is concave upward. Note: When using…

A:

Q: Find all values of the constants m and b for which the function S sin x, y : тx + b, х 2п is a.…

A:

Q: 3. Given x?y? = x² + y², find by implicit differentiation. dx

A: To find: The value of dydx. Given: The equation is x2y2=x2+y2. Formula used: Product rule of…

Q: iven: ƒ (x) = Ax? + Bx where A 6 and B= 5 ind: f' (x) using LONG METHOD DERIVATIVES.

A: We can find the answer as below

Q: Let fx) - V4X-3 vux-3 %3D O Find the arer age rate o ofe change in respect to x aver the intoy vel…

A:

Q: Q1. To solve this problem, you should use the function on the same line as your w value. w = 2 =…

A:

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: Which of the following is not correct regarding signs of derivatives A. If dy/dx>0, then the curve…

A: We are asked to find which statement is not correct.

Q: dy Find ck by implicit differentiation. √x+ y + √xy =4

A:

Q: dy c) Use implicit differentiation to find for 2xcosh (y)-In(tanh x)= y? dx

A: Given: 2xcosh-1y-lntanhx=y2   We know that; The Product rule: f·g'=f'·g+f·g' The chain rule:…

Q: Find the relative extrema of f(x) = (x − 1) cosh x − sinh x.

A: Maxima and minima: f(x)=(x-1)coshx-sinhx f'(x)=(x-1)sinhx+coshx-coshx f'(x)=(x-1)sinhx…

Q: Q4/ Evaluate (xy + e") dy dx using Three point formula in x,y-axis and two point formula in z axis

A: You must have an basic idea of double integral to solve this.

Q: Q5: If y= tant and x = cost then at t= is (not that these functions in N) dx a) -1 b)0 c) d) I e)…

A: