( 22 – 3z + 1, z < 3 14- 2, *23 valuate the following limits for h() = and Justify your answer.

Q: d Compute [(2x² + 5)(4.x –1)] at x = Со dr

A: To find: The value of  ddx2x2+54x-1at x=12. Concept used: Product rule of differentiation f·g'=f '·g...

Q: 1. * S(2 cot?0 – 3 tan²e) de A 2 cot O – 3 tan O + 3 O + C C - 2 cot O – 3 tan O + 3 O + C B 2 cot e...

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Q: Using integration by parts, the integral 2 f cot-1 x dx equals: 2 x cot-1x + In|x² + 1| + C - x cot-...

A: Topic = Integration

Q: х3+3x-4 x2 с 1 x² + 3 In x + 4x + C 3 A -x² + 3 In x – 4x + C 3 - 1 x² + 3 In x + 4x + C -x2 + 3 In ...

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Q: Find F' (÷) if F(x) = 2 cos-1 Vx. %3D

A: We will find the value of F'12 where Fx=2 cos-1x in the following step.

Q: Find the global minimum of the function f (x) 1 + x² on the interval (0, co0)

A: Given that f(x)= 1+x2.  And we find global minima on the interval (0, infinity).     Here i attached...

Q: Using an appropriate substitution, 8tan-1x the integral J dx equals: 1+x2

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Q: The solution of the given equation (1+x²) y' + 2xy = 4x² is: O y=[(4x^3)/(3(1+x^2))]+C(1+x^2) O y=[(...

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Q: The solution of the non-exact differential equation (x*e +5dy + (1 +2x²e")dx = 0 is: O x^2 e*y+Inlyx...

A: To determine the solution of the following non‐exact differential equation.x3ey+xydy+1+2x2eydx=0

Q: 2. Find when f(x) = x²e* has a horizontal tangent.

A:

Q: In exercises 1-23 solve the given differential equations: dy 1. = sin 5x %3D dx 2. etdy dx = 2x dy 3...

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Q: Which of the following best describes the function below? (3x ifxs2 x if 2<x f (x) =

A: Checking limits:When x approaches to 2 from left side:=limx→2- f(x)=limx→2- 3x2=3(2)2 =12When x app...

Q: If f(x) = 3 cot ' + 4, then find the value of f'(-1) is.

A:

Q: Question 28 Sin(1) – - -5 The Differentiation of f (t) =- 1+ 5t is- In(t) [In(1)]² A True B) False

A: f(t) = (1 +5t)/ lnt f'(t) = (5ln(t) - (1+5t)(1/t))/(ln(t))2 f'(t) = (5ln(t) - 1/t - 5)/(ln(t))2 so t...

Q: Jertical asymptotes at x = -4 and x = 3. x -intercepts at (1,0) and (5,0) ot mol h y -intercept at (...

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Q: Find an equation of the tangent line to the graph of h(x)= 2x-x'at the point (-2, 4). Write the equa...

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Q: Exercise 1 In each of the following, use Lagrange multipliers to find the critical points and the re...

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Q: 6. * 1 dx Vã (1-/x) 2 In I 1- x1/2 |+ C ! In I 1 -x1/2 | + C A C -2 In I 1-x1/2 | + C - In 1 1 - x/2...

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Q: Using an appropriate substitution, (cos-1(x)) e the integral f dx equals: V1-x2

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Q: A potato is launched vertically upward with an initial velocity of 124 ft/s from a potato gun at the...

A: Initial velocity is given as 124 ft/sec and the distance is given as function of time s(t). We will ...

Q: For f dw ,w = w-wa O w = u^(1/3) O w = u^3 %3D O w = u^(2/3) w = u O O

A:

Q: Trace the curve of the following equations by giving the a. Intercepts b. Symmetry c. Vertical Asymp...

A: Equation of a curve is giveny2=2x4-5x3+3x2+4x-20x2-3x+2

Q: 1. lim 10 2x+1 2. lim X2 *-1 3. lim 4. lim f(x) if f(x) =- if x 2-1 if x>0 if x s-1 if x>-1 5. lim f...

A: Since you have posted multiple questions as per our guidelines we are allowed to answer first three ...

Q: By completing the square, dx the integral f equals: 2x2+8x+10 tan¬1(x + 2) + C tan-1(x – 2) + C | th...

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Q: 4. Given the graph and function below, complete the table. Differentiable Continuous f'(x) Derivativ...

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Q: x² +2x +3 dx x' +3x² + 9x A In Ix³ + 3x² + 9xl + C ! In Ix3 + 3x2 + 9xl + C 4 3. D 2 In I x3 + 3x² +...

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Q: (Ь) n2n n=1 (0)

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Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate ...

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Q: III I The current population of St. Catharines is about 133000. Suppose a major devel- opment is pla...

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Q: Let f (x) et . Find a so that f'( a ) = 0. Hint: use the quotient Rule.

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Q: 2x + 6, r 6 is continuous at %3D I = 6. Justify the conclusion. (i) f(6)= (ii) lim f(r)= (iii) lim ...

A: The given function,  fx=2x+6,x&lt;612,x=6-x+24,x&gt;6

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved a...

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Q: y = V1 + t² dt

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Q: dy Find using implicit differentiation, for the equation a + = 11 is. da

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Q: = sec.x-/2 tan .x , find f' (=). %3D

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Q: de spaces in characters. * 4 Find the value of f'(-1) if ƒ (x)=- (3r² – 2.r + Your answer

A: Topic:- derivatives

Q: Question 30 Determine the second derivative of 2x³ + y²= 1 – 4 y A 6x ( y + 2)-! - 9xª ( y + 2 ) -3 ...

A:

Q: 16. 1+ Vx= x +a (16 + x³)ª * =- b(16 + x²)* x=)= + C 17. x* dx :(9x + 49)을-(9x + 49)을 +c V9x + 49 18...

A: As per bartleby guidelines we only give first question answers.

Q: Question 21 Evaluate the first derivative of the implicit function: 4x2 + 2xy + y² = 0 4x +y (A x +y...

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Q: 1. ADEF = AJKL Solve for the value of y Sy 150 D.

A: Congruency of triangle 

Q: 14 If f(x) = /* t² dt then f'(x) =

A:

Q: B. Use the figure at the right. 1. [- 5, - 3) 2. [- 4, - 2] 3. [-1, 2] 4. (3, 5] 5. [1, 4] 4. 3- 2- ...

A: Given

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j...

A: To find the unit vectors that satisfies the given conditions.

Q: Consider the parallelepiped with adjacent edges u = 9i + 6j + k v = i+j+7k w = i+ 6j + 6k Find the v...

A: The given equations are,  u=9i+6j+k v=i+j+7k w=i+6j+6k.

Q: - courses / MATH1200 / Current Activity / Worksheet 1 From the following results, determine whether ...

A: Topic:- application of derivatives and calculus

Q: Using an appropriate substitution, 3 the integral S dx equals: V1-4(x-1)2 3 sin-1(2x – 2) + C sin-1(...

A: We can find the integration as below using proper substitution.

Q: a) Determine the cosine of the angles of the triangle whose vertices are A(1, –-2, 1), B(3, 0, 2), C...

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Q: The derivative of the function y = e* In(cos x) is: y' = e*(In(cos x) – tan x) y' = e*(In(sec x) + t...

A: To find the derivative of the following function.y=ex lncos x

Q: xp, 10. S

A: ∫ 7e-xdx/ex ∫ 7dx/e2x ∫7e-2xdx 7e-2x/(-2) +c -7e-2x/2 +c  

Q: a) dt 9 =dx xVln x b)

A: