Do not use calculators. Approximated decimals are not accepted. k=3 Let j=8 Evaluate and Simplify the following expressions. Note: i = imaginary unit where 2 = -1. Show ALL your calculation work. Every step must be immediately clear. 20+5k

Q: For the function f(x): - 5x² + x - 7, evaluate and fully simplify each of the following. f(x + h) =…

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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: A) Find all value(s) of a such that lim f(x) does not exist [Select] B) Find all value(s) of b such…

A: Question 8 A) limx→1-f(x)=6≠limx→1+f(x)=4 limx→2-f(x)=-∞≠limx→2+f(x)=∞ answer: a=1 and a=2 only

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Q: Suppose 10 workers produce 500 units of commodity X and 20 workers produce 800 units of commodity X,…

A: The formulae of marginal product is        MP=change in firm's use of inputchnage in quantity of…

Q: Q3. Use the integral test to determine whether the series, n=1 divergent. 1 (n+1)√n+1 is convergent…

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Q: a. The plane through P(0,2,-1) normal to n=3i-2j-k

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Q: a. Show that f has a removable discontinuity at x = 3. x² - 7x + 12 f(x)= x - 3 x = 3

A: Removable discontinuity

Q: Consider the function f(x) = x²-4 x²+2x-8 (a) Find the x and y intercepts of f(x) (b) State the…

A: Explanation of the answer is as follows

Q: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

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Q: Find dy dx dy d.x = if 3y³t + t³y = 4 and d.t dx = 1 cos t

A: Given

Q: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

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Q: Problems: Solve the following differential equations: 9- (e + In y)dx + (+)dy=0 y

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: 2. The value of O True O False ¹/² is = √13 13

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Q: If A=(4,3,0), B=(2,3,4) and C= (5,6,2) find the dot product and find the angle between the vectors.

A: Dot product defined as  AB =|A| |B| cos x x is angle between A and B

Q: a. Show that f has a removable discontinuity at x = 3. x² - 7x + 12 f(x): x + 2 = x = 3

A: The given function is: fx=x2-7x+12x+2, x=3 Show that f has a removal discontinuity at x=3

Q: Finding Coterminal Angles In Exercises 25-28, determine two coterminal angles in radian measure (one…

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Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

A: The given integral is: I=∫x2+2x+1x2+12dx   As we know that; The Power Rule: ∫xndx=xn+1n+1+C And…

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Find an equation for the graph shown to the right. Type the equation in the form y = A sin (@x) or…

A: Given

Q: (1 + 1 1 + In(x) + - X (x+y)ln(x) - 5y = c dx = (5-In(x)) dy

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Q: Find the derivative y = x tan^¹x − In √√1 + x²

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Q: 5. Determine the area below f(x) = 10 - 2x² and above the line y = 3. 6. Determine the area bounded…

A: Given problem:- Determine the area below f(x) = 10 - 2x2 and above the line y = 3

Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

A: We have to find the solution of given D. E.

Q: Evaluate the integral dx fax √2x-x1

A: Given: I=∫dx2x-x2   As we know the common integral; ∫11-x2dx=sin-1x+C

Q: Find the limit by interpreting the expression as an appropriate derivative. e2x 1 lim- = i x→0 X

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Q: A number x is selected at random from the interval [4,20]. The probability density function for x is…

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Q: V A

A: ∫x1+x2dx=∫2u4+u2du=2·∫u4+u2du=2·∫2v24+v4dv=2· 2·∫v24+v4dv=2· 2·∫ -v4v2+2v+2+v4v2-2v+2dv=2·…

Q: 207 Σ=15 (11). Find sum Σ 15

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Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: Use implicit differentiation to find d²y = dx² d²y dx² if 8y+sin y = x.

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Q: 5. The points A(1, 0, 2), B(2, 0, 1) and C(1, 2, k) form a triangle of area √6. Determine the…

A: Follow the procedure given below.

Q: 4) Find equations for the planes: b. The plane through (1,-1,3) parallel to the plane 3x+y+z=7 A-3+1

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Q: Write the equation for a cosecant function satisfying the given conditions. period: 5x; range: (-∞,…

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Q: 6. 1 2 0 *(:) * (****)- 34 G 9 11 B. None of them A. C -11 D. 18 201

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Q: a) Using the methods of (a) Gauss elimination and (b) Gauss-Jordan, solve the following system of…

A: Since you have asked multiple questions,as per our guidelines we are supposed to answer only one…

Q: 2) Let u=5i-j+k, v=j-5k and w=-15i +3j-3k. Which vectors, if any, are: a. Perpendicular? b.…

A: To find out the vectors which are parallel and perpendicular.

Q: Determine whether the series converges. The series 8 k=1 13 15k

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Q: For the piecewise function f graphed below, find the following. y-axis 6 5 4 3 2 1 78 9 10 11 12 13…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: (b) (i) Identify the critical numbers of f. (Enter your answers as a comma-separated list.) X = (ii)…

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Q: Y=t-2√√√x + X Find domin and ringe

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Q: A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x…

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: Find the linearization of the function f(x) = 1 9x+8 √a la π sin (a) L(x)= Find the true values of f…

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Q: se the formula FV = PMT(1+i)-1 i

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Q: Q4A/ If y=x sinx+√1-x², then dy/dx is: 1.√1-x² sin-¹ x 2. sin(x) O 1 O 2 x cos(x) sin(x) sin(x)2

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Q: dy dx Using logarithmic differentiation, find NOTE: Express your answer in terms of x only. dy dx =…

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Q: -πl-π" ㅠㅠ Using the technique of substitution with u = • ITT -T, the terms of u as 1 -1 -1- du (a)…

A: This question can be solved using the concept of integration by substitution.

Q: Determine each of the following for the circle whose equation is ² The equation of the circle in…

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Q: derivative. (a) lim (b) lim Ax→0 In(e¹ + Ax) - 4 Ax In w w 1 w 1 =

A: Using L hospital rule