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The given statement is “The absolute value of any real number is positive”. The distance between the...From the given figure it is observed that, the angle ∠AOC and ∠COB makes a straight line. That is,...Calculation: The given statement is f(−x)=−f(x) for any function f(x)”. Consider the function...Definition: Third quadrant angle: “An angle is called third quadrant angle, if the angle lies in...Definition used: The solution of the linear equation ax+by=c is a pair of numbers, one for each...Given: The given statement is “The solution of the equation x2−2x=0 is x=2”. Calculation: Consider...It is a known fact that all trigonometric ratios are positive in the first quadrant (0° to 90°). The...A vector should have magnitude and direction. Let A and B are two vectors of magnitudes A and B...The given function is, y=2cosx and the point is (π,−2). Substitute x=π and y=−2 in y=2cosx....

Rule used: The exponent rule: a0=1 where a≠0. Calculation: Given that, the equation is 2x0=1....Result used: The imaginary unit −1 is denoted by the symbol j. In other words, j=−1 and j2=−1....Definition used: The exponential function is defined as y=bx, where b>0,b≠1 and x is any real...The given statement is, “To get the calculator display of the equation 2x2+y2=4, let y1=4−2x2.” Note...Procedure used: Procedure for Synthetic Division: “1. Write the coefficients of f(x). Be certain...Check the matrix operation as follows: 2[3−102]=[6−202][6−204]≠[6−202]LHS≠RHS Hence,...Consider the inequality 1<x<−3. The given inequality 1<x<−3 can be written as 1<x and...The ratio of 25 cm to 50 mm is computed as, 25 cm50 mm=250 mm50 mm=5 That is, the ratio of 25 cm to...Definition used: n terms: The nth term of the arithmetic sequence is given by an=a1+(n−1)d, where an...Formula used: The Basic Trigonometric Identity: tanθ=sinθcosθ. Calculation: The given identity is...Formula used: The formula for distance between any two points d=(x2−x1)2−(y2−y1)2. Calculation: Find...Formula used: The limit of a function f(x) is that value of the limit of the function approaches as...Differentiate y with respect to the x. y=ddx(3x2−5)dydx=3(2x)−5=6x−5 Slope of tangent of the curve...Given that the equation is ∫(3x2+1)5dx=16(3x2+1)6+C. Evaluate the left hand side of the given...Consider the give statement. Let the initial velocity of an object be v0. Since the horizontal...Formula used: The derivative of sinu is d(sinu)dx=cosududx. Calculation: Evaluate the derivative of...Formula used: Log rule for integration: ∫duu=ln|u|+C Calculation: The given integral is ∫dx1+2x....It is given that if the function is f(x,y)=2x2y−y22xy, then f(y2,x)=2xy4−x22x2y . Replace x=y2 and...Result used: Let ∑n=0∞a1rn be a geometric series of terms, the partial sums Sn represents the sum...Definition used: “A solution of a differential equation is a relation between the variables that...

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