Given the function f(x)= = Find the difference quotient Find f'(x) by determining lim f(x +h)-f(x) h h→0 Find f'(-2) (This slope should match the tangent line you drew above.) Find f'(0) Find f'(1) Graph the function f(x) are -2, 0, and 1. Clear All Draw: -1 2x² f(x +h)-f(x) h 2x² and draw the tangent lines to the graph at points whose x-coordinates 10+ 9 8 6 5 4 3 2 1 -1 -3 -4 -5. -7 -8 -2+

Q: Find  f(t). ℒ−1{1/(s - 7)3}

A: The inverse laplace tranform L-11s-73

Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x): |x-1| In its domain. a.…

A:

Q: H.W: show that the equations are homogeneous and solve: 1. (x+y)dy + (x - y)dx=0

A:

Q: Find all the second partial derivatives. f(x, y) = x³y² + 6x^y fxx (x, y) = {xy(x, y) fyx(x, y) (xin…

A: We want to find second order partial derivatives.

Q: (D³ - 2D³ – 2D² – 3D − 2) y = 0 - - -

A:

Q: 8 1 ₁ }(s) = = nº n=1 Show that finding the value of the Reiman Zeta for (2) is just the value Basel…

A:

Q: e²x 9e2 + 18e + 10 (d) / 5 dx

A: To evaluate: ∫e2x9e2x+18ex+10dx Substitute ex=u⇒exdx=du:…

Q: Given = (1 + x -- k) dy da 13 What is the value of k such that y is perpendicular to the curve y =…

A:

Q: Which statement describes this graph? 3 15- -10- -5-

A:

Q: f(x) g(x) XX 2 5 6 7 The graphs of the functions f and g are shown below. If h(x) = Y A Provide your…

A:

Q: g(x)=x-bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: We have to solve given Questions.

Q: For the function h whose graph is given, state the value of each quantity, if it exists. (If an…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others parts…

Q: Find two numbers whose sum is "a", if the product of one to the square of the other is to be a…

A: sum of two numbers is 'a', the product of one to the square of the other is to be maximum

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A:

Q: ind the regions where sinx Sx.f

A: Topic:- trigonometry

Q: 2√ty' =√1-y²

A:

Q: lim h→0 f(1+h)-f(1) B)-f(1) h 5/14 Correct where f(x) = 9x² + x - 4

A:

Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: If f(x, y) = 49 - 7x² - y², find fx(1,6) and f (1,6). Illustrate with either hand drawn sketches or…

A: Given problem:- If f(x, y) = 49 - 7x2 - y2 ,find fx(1, 6) and fy(1, 6). Illustrate with either hand…

Q: Given f(x,y)=x²y³-4y, find the directional derivative at the point (2,-1) in the direction of v=.

A:

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A:

Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

A: Recall:  V=∫abπf(x)2dx We have a=0, b=6, f(x)=e-x

Q: Show that a right triangle is formed by points ?(3,1,-1), ?(5,3,6), and ?(3,-5,0). If it does not…

A:

Q: A giant spherical-shaped snowball is melting. If the radius decreases at the rate of 0.5 in/min, now…

A:

Q: Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of…

A: Concept: Polar coordinates are  x=rcosθ , y=rsinθ Now adding the square of both the equation…

Q: Determine if the function f(x) is continuous and/or differentiable at x = 2? x+10 for 2≤x≤2 f(x) =…

A:

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: Find the partial derivatives of the following function: z = f(x, y) = e¹²¹² fx= fxx = fxy = fy= fy=…

A:

Q: tody + y² = 0 dt

A:

Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

A:

Q: Compute the following limit. 1-cos(z) as x approaches 0

A:

Q: Differentiate the function with respect to the independent variable. f(x)=-7x+5x³-6 f(x) =

A: Given, f(x)=-7x4+5x3-6

Q: 1 dx 49 1 42 49 arcsin 7x) - 49 sin 2 arcsin 7x+C (2x) 2 (1 x)) X

A: Given, ∫ x249-x2dx

Q: lim (SC - S(T)) where f(x) = -x²+x+6 f(7+h)-f(7) h h→0

A: f(x)=-x2+x+6= limh→0 f(7+h)-f(7)h limh→0 -(7+h)2+(7+h)+6-[-72+7+6]h limh→0…

Q: 5. fe²x sin x dx

A:

Q: Find the total number of permutations of the word 'ASSASSINATION', where all vowels are ALWAYS…

A: We have to find the number of ways

Q: Evaluate the determinant of the given matrix by reducing the matrix to row-echelon form. 4 -4 16 A =…

A:

Q: Determine whether the differential equation . (8x² − 2xy + 7) dx + (4y² − x² + 8) dy = 0 is exact.…

A:

Q: Describe the advantages and disadvantages of using linear scale axes versus logarithmic scale axes…

A:

Q: Find the area of the region described. 4 1 The region bounded by y = and y = - 1-x 2

A: To find the area bounded by the curves y=43&y=11-x2. The region bounded by the curves is:

Q: Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not…

A:

Q: Calculate the value of the following limits algebraically, (if they 2x-1 a) lim x+1 X² 2x²-9x-5 b)…

A: Topic:- application of calculus

Q: Find the equation of the tangent line to the curvey = 4 sina at the point (¹²). The equation of this…

A:

Q: (10. a = [-1, 5,2], b = [3, 2,-6], and c = [1, -4,-2]. Calculate the following: a) axb b) a b × c c)…

A:

Q: Let A(0, -2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA)=2. m(PB) (2) Convert the…

A: This question can be solved using the concept of distance formula.

Q: Find the value(s) of k that makes the given function continuous. (-x+2 if x < k f(x) = 4x + 3 if k ≤…

A:

Q: Write the first five terms of the sequence, give the exact answer: too n n+7 n=1 Determine whether…

A:

Q: J 6x x +3 dx

A:

Q: = f(x,y) = x² Determine whether the function z = (why or why not) +y + y² for for (x, y) = (0,0) (x,…

A:

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.